Dynamic Modeling, Simulation, and Flight Test of a Rocket

Research ArticleDynamic Modeling Simulation and Flight Test of aRocket-Towed Net System

Feng Han Qiao Zhou and Fang Chen

State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China

Correspondence should be addressed to Qiao Zhou bitzhouqiao126com

Received 25 December 2018 Revised 23 March 2019 Accepted 28 March 2019 Published 24 April 2019

Academic Editor Gregory Chagnon

Copyright copy 2019 FengHan et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Rocket-towed systems are commonly applied in specific aerospace engineering fields In this work we concentrate on the study ofa rocket-towed net system (RTNS) Based on the lumped mass method the multibody dynamic model of RTNS is establishedThe dynamic equations are derived by the Cartesian coordinate method and the condensational method is utilized to obtainthe corresponding second order ordinary differential equations (ODEs) Considering the elastic hysteresis of woven fabrics atension model of mesh-belts is proposed Through simulation in MATLAB the numerical deploying process of RTNS is acquiredFurthermore a prototype is designed and flight tests are conducted in a shooting range Ballistic curves and four essential dynamicparameters are studied by using comparative analysis between simulation results and test data The simulation acquires a goodaccuracy in describing average behaviors of the measured dynamic parameters with acceptable error rates in the main part ofthe flight and manages to catch the oscillations in the intense dynamic loading phase Meanwhile the model functions well as atheoretical guidance for experimental design and achieves in predicting essential engineering factors during the RTNS deployingprocess as an approximate engineering reference

1 Introduction

Rocket-towed systems [1ndash5] using rockets as power sourcebelong to a certain type of equipment applied in aerospaceengineering fields After launching the payload is towed bythe rocket out of its container and delivered to the targetterritory Engineers are capable of achieving remote controland rapid deployment with these systems In this paper wefocus our energy on the study of a rocket-towed net system(RTNS) which is one of the systems as stated above Thepayload part of the system is several units of flexible netwhichare arranged in the container beforehand

When designing the engineering factors a dynamicmodel of the deployment process is urgently needed to bedeveloped The dynamic process of RTNS mainly involvesmotions of the rocket the net and the connecting devicesbetween parts In exterior ballistics phase the rocket isaffected by engine thrust aerodynamic force gravity andother factors Meanwhile its movement is also coupled withthe flexible net and the connecting devices Combiningthe rigid-body swing motion of the rocket and the flexible

vibration of the net it is appropriate to apply multibodydynamics theories in RTNS modeling

Rocket-towed systems have been seldom studied beforeRocket-towed systems such as rocket-propelled remote ropeerection devices [1 2] and shaped charge array deployingdevices [3] were the main research targets in previousresearch Gu et al [1] presented a dynamic model of linethrowing rocket with flight motion based on Kanes methodthe kinematics description of the system and the forces actingon the system were both taken into consideration Lu et al[2] also applied Kanes method in developing a lumped massmodel of rescue rope which was divided into several discretefinite segments Djerassi et al [5] studied the deployment ofa cable from two moving platforms they proposed a modelof masses and the cable was regarded as a collection of linksMankala and Agrawal [6] studied the dynamic behavior ofa tether-netgripper system under impact The tether wasmodeled as a continuumand simulationwas finished by usingthe ordinary differential equation (ODE) solver in MATLAB

Throughout the studying history of linecable systemdynamics the continuum method and the multibody theory

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 1523828 21 pageshttpsdoiorg10115520191523828

2 Mathematical Problems in Engineering

are two mainstream modeling approaches adopted in theo-retical research and engineering applications Although thecontinuum method is considered to be more accurate themultibody theory represented by the lumped mass methodan emerging methodology in the research field of dynamiccharacteristics of flexible cablenet is more compatible tobe applied to complex multibody dynamics and computerprogramming Many other scholars continued applying anddeveloping lumped mass method in aerospace engineering[7ndash14] and ocean engineering fields [15ndash22]

Williams and Trivailo [7 8] studied the dynamics of acircling aircraft-towed cable system A lumped mass modelof the cable was built for the circularly towed configurationpractical towing solutions that achieve small motion of thetowed body were obtained by using constrained numeri-cal optimization Meanwhile they studied the transitionaldynamics as the aircraft changes from straight flight tocircular flight by assuming no tension in the cable Williamslead his team [9ndash12] in investigating the dynamic deploymentof aircraft-towed cable dropping systems They proposed azero-tension cable model by using lumped masses connectedvia rigid links and modified it by introducing the linearelastic tension hypothesis Then aerodynamic force actingupon the discrete links was considered when simulatingthe flight attitude of the cable and optimal control schemeswere presented through a parameterization study on essentialcontrol variables Trivailo and Kojima [13] developed thecomprehensive nonlinear models of following net capturingsystems for debris removal Dynamics of the net systemsand their interaction with the capturing objects were studiedSharf et al [14] presented a concept for a net closingmechanism they finished the design and testing of a debriscontainment system for use in a tether-net approach to spacedebris removal

Buckham et al [15ndash18] adopted a mass-spring model toreveal the dynamic behavior of the cable in a towed underwa-ter vehicle system by taking into account the cable viscosityFurthermore they introduced the flexural rigidity of thecable into the previous proposed model following GalerkinPrinciple Bending moment acting on the cable segment wastransformed to concentrated force imposed on the discretemass in order to increase the model accuracy in describingthe attitude of the cable under low-tension situations TakagiT et al [19ndash22] developed a net-configuration and load-analysis system under ocean current effect based on a mass-spring model

In this paper a lump-mass multibody model of RTNS isestablished by the Cartesian coordinate method in the case ofa two-dimensional assumption This model is involved in theelasticity of the wire rope flexible mesh-belts and retainingrope Due to the complex operating conditions we finishthe calculation of the initial RTNS position when the net isarranged in its container before launching By taking intoaccount the elastic hysteresis of woven fabrics we proposeda modified tension model of mesh-belts Furthermore aprototype of RTNS is designed and built Flight tests areconducted in a shooting range Ballistic curves and fouressential dynamic parameters are studied by using compar-ative analysis between simulation results and test data The

6 5 4 3 2

1

7

Figure 1 Rocket-towed net system 1 rocket 2 wire rope 3transition section 4 net 5 supporting bar 6 net container 7launching platform

simulation acquires a good accuracy in describing averagebehaviors of the measured parameters with acceptable errorrates in the main part of the flight and manages to catch theoscillations in the intense dynamic loading phase

2 Multibody Model

21 Deployment Process of RTNS As shown in Figure 1 RTNSis a quite complex set of devices It consists of a rocket anet part a launching platform (including a tractor and a netcontainer) and connecting devices (including awire rope anda retaining rope) between them

During the working process of RTNS the launching plat-form and the net container are almost stationary Thereforeas shown in Figure 2 the major research targets of RTNS arethe net the rocket and the connecting devices

As shown in Figure 2 the flexible fabric net is made ofsix net units and two transition sections Each unit contains4 longitudinal mesh-belts and 24 transverse mesh-beltsTwo transition sections refer to the front and back mesh-belts which connect the six units to the wire rope and theretaining rope The mesh-belts are woven from nylon Inevery longitudinal-transverse intersection there is a screwwhich connects the belts in orthogonal directions In orderto keep the net stretching out and tight longitudinally sevenequidistant transverse supporting bars are set at the frontback and middle of the net The bars link six net unitstogether Two ends of the net are connected to the rocketand the fixing device by the wire rope and the retaining roperespectively

The launching-flying-landing deployment process ofRTNS can be divided into four phases as follows

(1) The rocket is launched from the platform and startspulling the wire rope connecting behind it

(2) The net begins being towed out of the container unitby unit until the rocket engine finishes working

(3) RTNS continues flying forward with inertia until theretaining rope starts functioning

Mathematical Problems in Engineering 3

1234567

6000mm

1000mm

30800mm1000mm

4800mm

3000mm

Longitudinal direction

Tran

sver

se d

irecti

on

Figure 2 Net rocket and connecting devices 1 rocket 2 wire rope 3 front transition section 4 supporting bars 5 mesh belts 6 backtransition section 7 retaining rope

12345678

Figure 3 RTNS in flight 1 rocket 2 wire rope 3 supporting bars 4 mesh belts 5 transition section 6 retaining rope 7 net container 8fixing point

(4) RTNS lands on the ground Under the influence ofthe retaining rope and seven supporting bars the netis deployed on the target territory in a fully stretchedstate

Figure 3 indicates a certain moment of RTNS in flight

22 Two-Dimensional Assumptions The dynamic behaviorsof RTNS can be divided into three simultaneous types thelongitudinal deploying motion the transverse translationalmotion of the net and its rotation around the center longi-tudinal axis Obviously the large-scale displacement causedby the longitudinal deployment motion is much larger thanthe transverse one And effect resulting from the latter twomotions on the longitudinal motion is very little Withoutregard to transverse windage we can also neglect the rotationand consider no transverse disturbance during the rocketballistics phase due to the symmetry of RTNS Furthermoreas a result of lacking rigid support along the longitudinaldirection the longitudinal extension is expected to be muchmore considerable than the transverse one when we discussthe deformation in all parts of the system

Given the above that we have discussed the dynamicfeatures in longitudinal direction is the fundamental issue inthis paper Hereon we consider the launching-flying-landing

deployment process of RTNS as a two-dimensional subjectand introduce the following assumptions as follows

(1) Transverse translational motion is ignored(2) There is no aerodynamic force acting upon the system

during its flight(3) The thrust eccentric effect on the rocket is neglected

the ballistic curve sticks to one same coordinate plane(4) Velocity and force states in the net are highly consis-

tent transversely Directions of the vectors are alwaysparallel with the rocket trajectory plane

23 Multibody Model of RTNS Based on the assumptionsstated above it becomes viable to acquire a practical multi-body model of RTNS Firstly the wire rope the retainingrope and the net are handled as an integral flexible body Aseries of straight elastic bar segments associated end to end byundamped hinges are applied to substitute for the above bodyThe positions of transverse supporting bars coincide with theends of segments Then we divide the mass of each segmentevenly into both ends of it and remove all undamped hingesout of this model

At this point the wire rope the retaining rope and thenet have been modeled into a string of lumped masses linkedby massless elastic force elements between them These force


elements describe the longitudinal elasticity of the flexiblebody According to the longitudinal mechanical propertiesof the system value of each force element which equals thetension between lumped masses is calculated based on thetensile moduli of different materials Meanwhile each forceelement reacts along with the direction of its correspondingbar segment In particular when dealing with force elementswhich belong to the net part the cross-sectional area of thenet is taken as the total areas of all four mesh-belts in itsrelevant position Considering that the mesh-belt has almostno resist compression strength the tension force is assumedto be zero when the mesh-belt is compressed shorter than itsoriginal length

On the basis of RTNS configuration one end of theretaining rope is connected to the net the other end ismounted to the fixing device Correspondingly the lastlumped mass of the model remains stationary to the groundduring the whole working process The first lumped massin the string coincides with the joint of the wire rope andthe rocket as a result a fixed-end constraint is added in themultibody model

The rocket is regarded as a rigid body operating in a two-dimensional plane Displacement of the rocket is describedby its centroid coordinate and the angle between its axisand horizontal direction is chosen to reveal the rotationmechanism

Up to present RTNS has been built into a discretemechanical model composed of a string of lumped massesand the rigid rocket The dynamic characteristics of themare the crucial topic in analyzing the deployment processMoreover the rocket engine thrust gravity and tension forcesbetween lumped masses are generalized forces imposed onthe RTNS model

To derive the dynamic equations the Cartesian coordi-nate method is often applied in multibody dynamics [2324] Under the circumstance of this coordinate system theabsolute coordinates of the position and attitude are adoptedto constitute the dynamic equations Advantages of thisapproach can be summed up as follows

(1) Equations built by absolute coordinates possess aclarity of physical meanings

(2) The values of mass matrix elements remain constantwhich is vital to decouple equations during the courseof computer simulation procedure

(3) This method is more suitable for multibody systemswithin few kinematic constraints

In our case there is only one fixed-end constraint existingbetween the first lumped mass and the bottom center of therocketTherefore we select the Cartesian coordinate methodto investigate the model

On the basis of a Cartesian coordinate system the inertialreference frames of RTNS are set and shown in Figure 4With x-axis and y-axis along the horizontal and verticaldirections respectively we define the first supporting barrsquosmapping point on the ground before launching as the originof coordinates

Y

X

O

Mi (xi yi)

M1 (x1 y1)

C (x0 y0)

P (xd yd)

0

Force element

Figure 4 Inertial reference frames of RTNS

The angle 1205790 between rocket axis and horizontal directionalong with the absolute position coordinates of the rocketcentroid 119862(1199090 1199100) and lumped masses 119872119894(119909119894 119910119894) is markedin Figure 4 When numbering the subscripts of coordinatesthe lumped mass located at the bottom center of the rocket isspecified as 119875(119909119889 119910119889) and then the subscripts of the followingmasses are made in turn starting from 1 to N To sum upthe whole flexible part of the wire rope the retaining ropeand the net is divided into N segments The total number ofgeneralized coordinates expressed in (1) is 2N+5

q = [119909119889 119910119889 1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873]119879 (1)

3 Dynamic Equations

31 Derivation of Equations To a kinetic multibody systemcontaining n generalized coordinates

q = [1199021 1199022 sdot sdot sdot 119902119899]119879 (2)

The universal dynamic equation in a variational form can beexpressed as

119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 0 (3)

where 119876119868119898 and 119876119890119898 are the generalized inertia force andgeneralized force of the generalized coordinate (denotedas 119902119898) respectively Supposing the mutual independencebetween all n generalized coordinates due to the fact thatthe variation of generalized displacement 120575119902119898 is arbitrary(3) only holds under the circumstance that the coefficientsof 120575119902119898 are identically equal to 0 We can obtain the dynamicequations composed of n formulae

119876119890119898 + 119876119868119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (4)

However almost all kinds of engineering equipmentincluding RTNS contain constraints S mutual independentconstraints existing in the system can be expressed as

119862119894 (q 119905) = 0 (119894 = 1 2 sdot sdot sdot 119904) (5)


Consequently then generalized coordinates are no longercompletely independent and dynamic equations of the systemcould not be set up directly from (4) To cope with thissituation the Lagrange multiplier method is adopted inour study [25] Following the skeleton of this methodologyconstraint functions are converted to penalty functions andembedded into the variational principleThe variational formof (5) derived by variational calculation is

119899sum119898=1

120597119862119894120597119902119898 120575119902119898 = 0 119894 = 1 2 sdot sdot sdot 119904 (6)

S Lagrange multipliers indicated by 120582119894 are put to use inestablishing the penalty functions Then we introduce thepenalty functions into the universal dynamic equation ( (3))

119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 119904sum119894=1

(120582119894 119899sum119898=1

120597119862119894120597119902119898 120575119902119898)

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 minus 119899sum119898=1

119904sum119894=1

120582119894 120597119862119894120597119902119898 120575119902119898 = 0

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898)120575119902119898 = 0

(7)

As is shown in (7) with an applicable group of 120582119894s coefficients of 120575119902119898 are equal to 0 keeping the rest n-sgeneralized coordinates mutually independent In order tomaintain (7) tenable values of the other (n-s) coefficients areprescribed as 0

119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (8)

Equation (8) is well known as the Lagrange equation ofthe first kind

With the existence of n generalized coordinates and sLagrange multipliers there are (n+s) unknown quantities ofthe kinetic multibody system Combining (5) and (8) theclosed multibody dynamic equations are

119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898 = 0 (119898 = 1 2 sdot sdot sdot 119899)119862119894 (q 119905) = 0 (119894 = 1 2 sdot sdot sdot 119904)

(9)

In the following part of this subsection the absolutecoordinate expression of (9) in the Cartesian coordinatesystem shown in Figure 4 is fulfilled in preparation forsubsequent computational simulation As can be indicatedfrom Section 23 above only one fixed-end constraint existsin the RTNS multibody model the constraint equations canbe expressed as follows

C = [1199090 minus 1198970 cos (1205790) minus 1199091198891199100 minus 1198970 sin (1205790) minus 119910119889] = 0 (10)

where 1198970 is the distance from the rocket centroid to bottomcenter The Jacobi matrix of (10) is expressed as

Cq = [minus1 0 1198970 sin (1205790) 1 0 0 sdot sdot sdot 00 minus1 minus1198970 cos (1205790) 0 1 0 sdot sdot sdot 0] (11)

According to (10) there are two Lagrange multipliersdenoted as 120582 (120582 = [1205821 1205822]119879) The multibody dynamicequations of RTNS are

Mq + Cq119879120582 = F


whereM is the mass matrix F is the generalized force matrixIt contains the moment of the resultant external force actingon the rocket and the resultant external forces imposed onlumped masses and the rocket

M = diag (119898119889 119898119889 1198690 1198980 1198980 1198981 1198981 sdot sdot sdot 119898119899 119898119899) (13)

F

= [119865119889119909 119865119889119910 1198720 1198650119909 1198650119910 1198651119909 1198651119910 sdot sdot sdot 119865119899119909 119865119899119910]119879 (14)

Apart from gravity G119894 each lumped mass is also affectedby the forcewhich is signified as T119894 of its adjacent forceelement Specifically T119894 is defined as the elastic force imposedfrom the ith force element on the ith dumped mass Mean-while the rocket is boosted by its engine thrust F119903 It is worthnoting that the moment and the force imposed from the wirerope on the rocket namely the restriction caused by thefixed-end constraint as mentioned earlier do not correlatewith F For this reason in (10) we have 1198720 = 0 Thegeneralized force acting on the rocket is

F0 = [1198650119909 1198650119910]119879 = F119903 + G0 (15)

The generalized force acting on each lumped mass is

F119894 = [119865119894119909 119865119894119910]119879 = G119894 + T119894 minus T119894+1

(119894 = 1 2 sdot sdot sdot 119899 minus 1) (16)

Equation (16) works on all lumped masses with theexception of the first and last individuals which refer to thetwomasses coinciding with the front end of wire rope and theback end of retaining rope respectively Both of them receiveonly one tension force in a single direction

F119889 = [119865119889119909 119865119889119910]119879 = G119889 minus T1 (17)

F119899 = [119865119899119909 119865119899119910]119879 = G119889 + T119899 (18)

Equation (12) is a typical example of differential-algebraicequations (DAEs) which are frequently engaged in theresearch field of multibody dynamics With both secondorder ODE and algebraic equation as its constituents DAEs


could not be solved directly It is essential to transform (12)into a set of authentic second order ODEs In the interest ofthis issue we adopt the contracted method to eliminate theLagrange multipliers 120582 and all nonindependent generalizedcoordinates [26]

Constraint relations between five generalized coordi-nates including 1199090 1199100 119909119889119910119889 and 1205790 are given in (10) Takingthis into account we can choose any two coordinates of themas nonindependent coordinates and represent the two withother independent ones In our case (1199090 y0) referred to asthe joint of the wire rope and the rocket are selected

Large-scale matrices in multibody dynamics are fre-quently rewritten into block matrix forms Matrices in thisform are more concise and clear making it more feasiblefor researchers to disclose relations between independentand nonindependent coordinates Therefore the generalizedcoordinate matrix q and the Jacobi matrix Cq are expressedby nonindependent and independent block matrices

q = [q119889 q119894]119879 (19)

Cq = [Cq119889 Cq119894] (20)

where subscripts 119889 and 119894 denote the nonindependent andindependent matrix elements respectively and

q119889 = [119909119889 119910119889] (21)

q119894 = [1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873] (22)

Cq119889 = [minus1 00 minus1] (23)

Cq119894 = [ 1198970 sin (1205790) 1 0 0 sdot sdot sdot 0minus1198970 cos (1205790) 0 1 0 sdot sdot sdot 0] (24)

By derivation of (10) the velocity constraint equationsand the acceleration constraint equations are derived andtransformed in block matrix forms

Cq119889q119889 + Cq119894q119894 + C119905 = 0 (25)

Cq119889q119889 + Cq119894q119894 + (Cqq)q q + 2Cq119905q + C119905119905 = 0 (26)

where subscript 119905 indicates the time partial derivativesthe term (Cqq)q in (26) represents the Jacobian matrix ofCqqto q Here we define 120573 as

120573 = (Cqq)q q = [[021198970 cos 1205790021198970 sin 1205790

]]

(27)

Equation (26) indicates the relation between the indepen-dent accelerations q119894 and the nonindependent accelerationsq119889 Substituting (23) in (26) we have

q119889 = minusCq119889minus1Cq119894q119894 minus Cq119889

minus1120573 = Cq119894q119894 + 120573 (28)

Therefore the nonindependent accelerations (q119889) areeliminated

q = Aq119894 + b (29)

where

A = [Cq119894

I] (30)

b = [1205730] (31)

Substituting (29) in the second order ODEs of (12) wehave

M (Aq119894 + b) + Cq119879120582 = F (32)

whereM and F in block matrix forms are

M = [M119889 00 M119894

] (33)

F = [F119889F119894

] (34)

By left-multiplying (32) by A119879 the Lagrange multipliersare eliminated

(Cq119894119879M119889Cq119894 + M119894) q119894 = F119894 + Cq119894

119879F119889 + Cq119894119879M119889120573 (35)

Up to now (12) is converted into (35) from DAEsto second order ODEs Equation (35) containing 2N+3equations is the contracted multibody dynamic equations ofRTNS It is noteworthy that among all the matrix elementsin Cq119894

119879M119889Cq119894 only the ones of the 3times3 block in the top leftcorner are nonzero Thus Cq119894

119879M119889Cq119894 is a large-scale sparsematrix Meanwhile M119894 is a diagonal matrix As a result themass matrix of (35) namely (Cq119894

119879M119889Cq119894 + M119894) possessesa comparatively low nonlinear degree which is a significantproperty in computational programming and simulation

32 Generalized Force

321 Rocket Thrust In Section 22 we assume no thrusteccentric effect on the rocket Therefore the thrust operatesalong with the axis of the rocket Through the time-historycurve 119865(119905) of the rocket thrust recorded in the engineeringmanual we have

F119903 = 119865 (119905) sdot n (1205790) (36)

where F119903 is the rocket thrust matrix and

n (1205790) = [cos 1205790 sin 1205790]119879 (37)

322 Tension Force The force elements proposed in thelumped mass multibody model reveal the tensile capacity ofRTNS in the longitudinal direction For instance the originallength of the ith bar segment is 119897119900119894 After extension the lengthturns into

119897119894 = 1003816100381610038161003816riminus1 minus r1198941003816100381610038161003816 (38)


(a) (b)

Figure 5 Material test of the mesh belts (a) material test system (MTS) (b) a sample under test

where riminus1 and r119894 are the position vectors of the (i-1)th and theith lumpedmasses respectively when 119894 = 2 3 sdot sdot sdot 119899minus2 119899minus1Particularly when 119894 = 1 r0 is the position vector of the rocketcentroid

Based on the discussion in Section 23 119879119894 = 0 when 119897119894 lt119897119900119894 We assume that the tension and the strain exhibit a linearelastic response in all flexible parts of RTNS According to theengineering strain theory 119879119894 can be expressed as

119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)

where 119897119894 is the real-time length of the ith force element 119897119900119894is the origin length of the ith force element 119864119894 is the tensilemoduli and 119860 119894 is the cross-sectional area of all four mesh-belts in the ith segment Both119864119894 and119860 119894 contain three differentvalues corresponding to the wire rope the restrain rope andthe net respectively The elastic force vector imposed fromthe ith force element on the ith dumped mass is

F119879119894 = 119879119894 sdot riminus1 minus r119894119897119894 (40)

Obviously the one from the ith force element on the (i-1)thdumped mass is minusF119879119894 due to Newtonrsquos third law

In (39) the flexible parts of RTNS including the wirerope the restrain rope and the net are considered to belinear elastic materials However since the mesh belts are themain components of the net the woven fabric structure in thebelts should not be overlooked Ordinarily the constitutiverelations of woven fabric materials are quite different fromthose of other engineering materials [27ndash30] on the onehand the inner structure of the belts remains slack undernatural conditions as a result of this feature there is apretightening stage during the initial phase of deformationon the other hand the stress-strain curve varies in the processof continuous loading and unloading due to the elastichysteresis of woven fabrics

400

300

200

100

0

Stre

ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N

Figure 6 Stress-strain curve of the sample under three cycles themaximum loads for three cycles are 3000N 5000N and 7000N

As is shown in Figure 5 an experiment study onmechan-ical performance of the mesh belts is accomplished under thesupport of a material test system (MTS)

First we load the testing force up to 3000N and unloadit down to 100N with a constant rate then we repeat theloading-unloading cycle several times to finish the experi-ment Figure 6 shows the stress-strain curve of the sampleunder three cycles It is clearly that the unloading-stagestress is much lower than the loading-stage one which isa remarkable manifestation of elastic hysteresis phenomenaEnergy loss occurs in every load-unload cycle

In view of the experimental data we find that the stress-strain relationship of the mesh belts is quite complicatedand engineering strain is not suitable in our case In thiswork consideration is given to both compatibility of (39)and elastic hysteresis of woven fabrics while modifying thetension model of mesh-belts A hysteresis coefficient 119886 isproposed to introduce the elastic hysteresis into the linear


(a) (b)

Figure 7 Net arrangement before launching (a) 3D schematic representation (b) 2D cross-section Blue parts denote the supporting barsred parts denote the net units and black parts denote the container

bracing force

frictionforce

gravity

Figure 8 Force analysis of the net

elastic model the tension force expressed in (39) can bemodified as

119879119894 =

119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 119897119900119894 119889119897119889119905 ge 0119886119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 119897119900119894 119889119897119889119905 lt 00 119897119894 lt 119897119900119894

(41)

where 119886 is based on the average energy loss ratio in all load-unload cycles The tensile modulus is modified to 119886119864119894 whenthe mesh belts are contracting

Similarly since the retaining rope is composed of highstrength fabric material the tensile modulus is also modifiedby adding a coefficient 119886 In this work 119886119899 = 037 119886119903 =023where 119886119899 and 119886119903 denote the hysteresis coefficients of thenet and the retaining rope respectively

323 Gravity Gravity in the Cartesian coordinate system isexpressed as follows

G119894 = [0 minus119898119894119892]119879 (42)

33 Construction of the Initial State Initial values of general-ized speeds (q0) and generalized coordinates (q0) ought to begiven while solving (12) Initial generalized speeds are 0 sincethe initial time (119905 = 0) refers to the moment in which theengine starts As for q0 constructing the initial state underthe actual operating conditions needs to be conducted Asis shown in Figure 7 the net is arranged in its containerand stays at a static draped state before launching Transversesupporting bars in the net are hung on the slide rails on bothsides of the container isometrically

Study on the initial state is divided into two steps firstthe initial positions of all lumped masses in RTNS areacquired by solving out the static draped state after thatinitial constraints are presented in order to keep the systemstationary before launching

331 Initial Positions Since the net part is made up of themesh belts and the supporting bars we consider them as oneintegral object and carry out a force analysis of the net at thestatic draped state As is shown in Figure 8 the supportingbars reach an equilibrium status by gravity the friction forcesand the bracing forces The mesh-belts are kept free-drapedunder gravity and the tension force


transition section

retaining ropefixing point

PC

Y

O X

supporting bar

wire rope

Figure 9 Initial position of RTNS

The net is separated into six units by seven supportingbars Constructions and stress states in all units are identicalbefore launching So it is reasonable to solve the drapedstate of one certain unit and get access to all positions ofthe lumped masses by coordinate translations Apart fromthe lumped masses coinciding with the supporting bars theposition coordinates of other lumped masses still satisfy (12)

Taking one single net unit as the research object wemake(119909119894 119910119894) as the position coordinates of the ith mass in the unitTwo formulae representing static equilibrium conditions areintroduced into (12)

Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)

Equation (43) is the static equilibrium equation of the netunit It can be solved by the Newton method

Similarly the initial positions of all lumped masses inRTNS (shown in Figure 9) are acquired by applying the aboveapproach

332 Initial Constraint Principle During the computationalsimulation initial constraints ought to be imposed on thelumped mass multibody model On the basis of the actualdeployment process an initial constraint principle is definedas follows every lumped mass is fixed by initial constraintsand remains stationary until the x-component of its resultantforce turns to a positive value It is worth noting that theresultant force mentioned above does not include the innerconstraint force caused by (10)

The initial constraints imposed on the supporting barscan be expressed as

q119887 = [q1198871 q1198872 sdot sdot sdot q1198877]119879 = 0 (44)

where q119887 is one part of q in (1) representing the generalizedcoordinates of seven supporting bars

After adding the initial constraints on the supportingbars the static draped states of the wire rope the net andthe retaining rope can be settled due to the static equilibriumequation ((43) in Section 331) So we do not need to setup initial constraints for other parts in RTNS Accordingto the initial constraint principle when conducting integraloperation of the multibody dynamic equations ((43) inSection 31) we check in every time step to decide whetherto exert the initial constraint forces over the supporting bars

4 Simulation

Based on the lumpedmassmultibodymodel proposed abovethe dynamic deployment process of RTNS is manifestedthrough self-programmed codes in MATLAB Calculationparameters such as the tensile moduli and the longitudinallinear density of the wire rope the net and the retaining ropeare determined in accordance with the actual engineeringdesign and experimental data of material tests The initialstate is constructed by the method proposed in Section 33All calculation parameters applied in numerical examples areshown in Table 1

As stated above in Section 31 the mass matrix of thedynamic equations possesses a low nonlinear degree Bytaking into consideration both low nonlinear degree in (35)and relatively short duration of RTNS deployment processone-step integral methods are able to ensure the precisionof simulation results In this workrsquos solution the classicalfourth-order Runge-Kutta method is applied to solve theODEs presented in (35) A 10minus6119904 step size is chosen under theconsideration of both precision and time cost

Figure 10 shows the simulation result of the launching-flying-landing deployment process where the green linedenotes the rocket the black line denotes the wire rope thepink lines signify the front and back transition sections thered line signifies six net units and the yellow line denotes theretaining rope

5 Flight Test

For the sake of validating the accuracy of the lumped massmultibody model a prototype of RTNS is developed andsuccessfully deployed in a flight test at a shooting range


10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

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8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

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8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

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(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s

Figure 10 Simulation results of the launching-flying-landing deployment process

Table 1 Calculation parameters

Parameter Unit Value Parameter Unit ValueRocket mass kg 4 Rocket moment of inertia Nm2 00832Transition section linear density kgm 1112 Rocket thrust N 1176Propellant burning time s 18 Rocket launching angle ∘ 15Wire rope cross-sectional area mm2 5846 Wire rope tensile modulus GPa 208Wire rope linear density kgm 0507 Net longitudinal linear density kgm 3168Mesh belt longitudinal tensile modulus GPa 357 Equivalent net longitudinal cross-sectional area mm2 3825Retaining rope longitudinal linear density kgm 048 Retaining rope longitudinal tensile modulus GPa 357Retaining rope cross-sectional area mm2 420 Supporting bar mass kg 121


(a) (b) (c)

Figure 11 RTNS prototype (a) its installation before launching (b) rocket (c) net

1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘

Figure 12 Layout of the test site 1 fixing device 2 net container 3 rocket 4 surveyors pole 5 high-speed camera

Figure 11 shows the RTNS prototype and its installationbefore launching

The test parameters are made consistent with the cal-culation parameters in Table 1 to ensure the comparabilitybetween the simulation and the flight test The layout of thetest site is shown in Figure 12

Flight tests for the same prototype are conducted follow-ing the identical experiment layout and repeated for six timesAll six runs of theRTNSprototype are recorded by a Phantomhigh-speed camera Figure 13 shows the whole deploymentprocess

Ballistic curves of all six runs are indicated in Figure 14Meanwhile test results including flight time ballistic peakpoint and shooting range (denoted as 119879119891 119884max and 119883max)are listed in Table 2 which are three essential factors to assess

how well the RTNS prototype meets its engineering aims Ascan be seen in Figures 13 and 14 the rocket is launched atthe top of the platform the net is pulled out and successfullydeployed to the target territory at a fully expanded state inevery shot The consistency of essential engineering factors isacceptable Experimental fluctuations of flight time ballisticpeak point and shooting range between all runs are 016s086m and 061m respectively It can be concluded that theprototype functions well in meeting the engineering aims inthe deploying process

However an experimental fluctuation analysis is notnegligible Out flied tests of a complex device such asRTNS are usually intervened by external working conditionresulting in the fluctuation between the experiment dataAs can be seen in Figure 14 ballistic curves of different


Table 2 Essential engineering factors of all runs

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6119879119891 280s 273s 268s 284s 271s 275s119884max 1141m 1118m 1076m 1102m 1055m 1110m119883max 3980m 3949m 3935m 3996m 3988m 3976m

(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test

runs begin to diverge right after the launching and presentfluctuations during the first half stage In the second halfperiod the curves become steady gradually along with therocket approaching the peak point and then differ againbefore the rocket landing

The rockets operated in the flight tests are all expendableone-time products using solid propellant engines Subtleflaws occur in the microstructure of the propellant aftera relatively long period of storage in a seaside warehouseConsequently small changes in chemical properties of thepropellant are inevitable which leads to distinctions in burn-ing rate and burning surface between different rockets duringthe preliminary stage of propellant combustion Thereforethere are minor differences existing between the outputthrusts of different rockets in the initial trajectory As a resultballistic curves present fluctuations during the first half stage

Aerodynamic force is considered to be another elementwhich causes the fluctuation in the ending period After the

engine stops working at t=18s the rocket starts to descendtowards the ground aerodynamic force is no more ignorableand turns into themain disturbance source affecting the flightstability and attitude of the rocket Consequently a landingpoint 061m fluctuation occurs under different wind scalecircumstances

6 Discussion

Several essential factors in the RTNS deployment process arediscussed Ballistic curve pitching angle centroid velocity ofthe rocket and the wire rope tension are investigated throughcomparisons between numerical simulation results and flighttest data

In Figure 15 ballistic curves of simulation and six flighttests are manifested As can be seen the ballistic simulationmatches the test ballistics well Based on three essentialengineering factors shown in Table 2 the error ranges in


Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)

Figure 14 Ballistic curves

Run 1Run 2Run 3Run 4

Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)

Figure 15 Comparison of ballistic curves between flight tests and simulation

flight time ballistic peak point and shooting range betweensimulation and Run1sim6 are -002sim+011s -057msim+029mand -39sim-33m (-07sim+41 -50sim+275 and -98sim-84 relatively) The small error ranges indicate the valuableaccuracy of our model in predicting the engineering factorsof RTNS

However an eccentric reverse occurs at the terminalballistic simulation resulting in the -39msim-33m landing-point error range between the simulation and the testsThis abnormal phenomenon is mainly caused by deficienciesexisting in the tension model ((41)) Though the constitutiverelations of the mesh belts and the retaining rope can beapproximately simulated by the modified tension model itis found that the simulation stress value at the low strainstage is exhibited remarkably higher than reality Thereby thesimulation stiffness of the retaining rope becomes larger thanits real value The unusual large stiffness magnifies its bufferaction on the rocket and causes the eccentric reverse in thenumerical example

Moreover the temporal synchronization of the modelin describing the RTNS deploying process is evaluated andconsidered qualified The average relative errors in real timeflight distances (longitudinal X values at the same moment)between Run1sim6 and simulation are 82 54 5759 71 and 127 respectively

The agreements on the attitude and velocity of the rocketbetween simulation and all six flight tests are studied based

on a time correlation analysis Time-variation curves offour essential dynamic parameters (including the resultantvelocity of the rocket centroid the longitudinal velocity of therocker centroid the horizontal velocity of the rocket centroidand the rocket pitching angle) are shown in Figures 16ndash19Furthermore Tables 3ndash6 reveal the statistical correlationsbetween simulation results and fight tests Correlation coef-ficients between the curves shown in Figures 16ndash19 are listedin these tables right after each figure correspondingly

As can be observed in Figures 16ndash19 four parametersindicating dynamic characteristics of RTNS all undergoa constant oscillation course during the whole deployingprocess Therefore when assessing the performance of themodel the RTNS operation is divided into four particularphases based upon different levels of agreements on the time-variation curves between simulation and tests Both accura-cies in predicting average behaviors and catching oscillationsof the measured parameters are taken into considerationphase by phase

With several characteristic times (as 119905119908 1199051 1199052 and 1199053marked in Figures 16ndash19) defined in four phases connec-tions between the oscillations in simulation and real testphenomena are studied Moreover listed out as statisticalsustains Table 7 shows key engineering elements emerging inflight tests and simulation to help in assessing the oscillation-catching accuracy of the model and Tables 8ndash11 provideaverage values of themeasured parameters in different phases


Table 3 Correlation coefficients between resultant velocities of the rocket centroid in tests and simulation

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Phases (1sim3) Simulation Phase 4Run 1 10000 08391 08293 08293 08464 08362 07051 02212Run 2 08391 10000 08463 08254 08370 08696 06975 02187Run 3 08293 08463 10000 08687 08848 08532 07415 01666Run 4 08293 08254 08687 10000 08491 09010 07059 02360Run 5 08464 08370 08848 08491 10000 08302 07002 02171Run 6 08362 08696 08532 09010 08302 10000 07156 02554

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(b) Run 2

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

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(d) Run 4

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(e) Run 5

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(f) Run 6

Figure 16 Comparisons of resultant velocities of the rocket centroid between flight tests and simulation

to help in assessing the accuracy of the model in predictingaverage behaviors

Phase 1 is characterized from 1199050 = 0 to 1199051 = 05119904where 1199050 = 0 represents the ignition time when the systemstarts working and 1199051 = 05119904 denotes the moment whenfirst of the six net units is fully pulled out of the containerCompared with the follow-up phases time-variation curvesof four dynamic parameters in Phase 1 go through a high-frequency and large-amplitude oscillation course The rocket

experiences a constant intense disturbance imposed by thepulled-out ending (exit in front of the container) of the netpart when flying forward and towing the net units The stressvalue of the disturbance is proportional to the mass inertiaof the stationary net ending which is being pulled out ofthe container That is to say sudden changes in longitudinallinear density of the pulled-out ending lead to the loadingoscillations on the rocket As can be inferred in Table 1 andFigure 3 the rocket successively pulls out the wire rope


403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(a) Run 1

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

Ｎ2 Ｎ3

ＮＱ

Ｎ1

(b) Run 2

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(d) Run 4

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(e) Run 5

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(f) Run 6

Figure 17 Comparisons of longitudinal velocities of the rocket centroid between flight tests and simulation

Table 4 Correlation coefficients between longitudinal velocities of the rocket centroid in tests and simulation


Table 5 Correlation coefficients between horizontal velocities of the rocket centroid in tests and simulation

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Phases (1sim3) Simulation Phase 4Run 1 10000 08938 08803 08904 08907 08932 07624 -02266Run 2 08938 10000 08785 08878 08898 08916 07609 -02555Run 3 08803 08785 10000 08730 08774 08764 07722 -02279Run 4 08904 08878 08730 10000 08881 08891 07542 -02676Run 5 08907 08898 08774 08881 10000 08911 07581 -02191Run 6 08932 08916 08764 08891 08911 10000 07577 -02553


20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

Ｎ2Ｎ3

(a) Run 1

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

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ＮＱＮ1

Ｎ2Ｎ3

(b) Run 2

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

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troid

(ms

)

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time (s)

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ＮＱＮ1

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(c) Run 3

20

10

0

minus10

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horiz

onta

l velo

city

of

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ocke

t cen

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(ms

)

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time (s)

Run 4Simulation

ＮＱＮ1

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(d) Run 4

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

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(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱＮ1

Ｎ2Ｎ3

(e) Run 5

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱＮ1

Ｎ2Ｎ3

(f) Run 6

Figure 18 Comparisons of horizontal velocities of the rocket centroid between flight tests and simulation

Table 6 Correlation coefficients between rocket pitching angles in tests and simulation

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Phases (1sim2) Simulation Phases (3sim4)Run 1 10000 08640 08418 08460 08392 08244 06096 02072Run 2 08640 10000 08510 08515 08464 08432 06008 02364Run 3 08418 08510 10000 08764 08736 08774 06160 01922Run 4 08460 08515 08764 10000 08471 08395 06130 02353Run 5 08392 08464 08736 08471 10000 08591 06024 02286Run 6 08244 08432 08774 08395 08591 10000 06685 02523

Table 7 Comparisons of key engineering elements between flight tests and simulation

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Error range119905119908(s) 0212 0214 0197 0210 0208 0218 0194 -0024sim-0003119881119877max(ms) 3687 3904 3899 3620 3799 4104 3510 -594sim-11119881119877119909max(ms) 3422 3617 3555 3378 3607 3880 2966 -914sim-412119881119877119910max(ms) 1520 1469 1600 1564 1477 1406 1877 +277sim+471


806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

Ｎ2 Ｎ3

rock

et p

itchi

ng an

gle (

∘ )

(a) Run 1

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 2Simulation

rock

et p

itchi

ng an

gle (

∘ )

(b) Run 2

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 3Simulation

rock

et p

itchi

ng an

gle (

∘ )

(c) Run 3

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 4Simulation

rock

et p

itchi

ng an

gle (

∘ )

(d) Run 4

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 5Simulation

rock

et p

itchi

ng an

gle (

∘ )

(e) Run 5

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 6Simulation

rock

et p

itchi

ng an

gle (

∘ )

(f) Run 6

Figure 19 Comparisons of rocket pitching angles between flight tests and simulation

Table 8 Average values of the resultant velocity (ms) in different phases

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Error ratePhase 1 2154 2199 2209 2157 2158 2198 1978 -105sim-82Phase 2 1613 1615 1596 1627 1623 1620 1663 +22sim+42Phase 3 1409 1394 1414 1391 1412 1403 1395 -13sim+03

Table 9 Average values of the longitudinal velocity (ms) in different phases

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Error ratePhase 1 1935 1986 1990 1944 1947 1986 1703 -144sim-120Phase 2 1580 1581 1555 1589 1579 1584 1591 +01sim+23Phase 3 1057 1035 1050 1034 1056 1048 981 -86sim-64

Table 10 Average values of the horizontal velocity (ms) in different phases

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Error ratePhase 1 878 873 881 863 880 872 973 +104sim+128Phase 2 283 286 285 293 290 287 324 +106sim+144Phase 3 -880 -887 -888 -884 -884 -878 -866 +14sim+25


Table 11 Average values of the rocket pitching angle (∘) in different phases

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Simulation Error ratePhase 1 3066 3062 2994 3107 3102 3073 2459 -209sim-179Phase 2 2882 2851 2898 2866 2869 2922 2829 -32sim-08Phase 3 1964 1848 1950 1968 2000 1915 1397 -302sim-244

12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)

Figure 20 Wire rope tension in simulation

the transition section and the first net unit therefore thelongitudinal linear density of the pulled-out ending increasestwo times in Phase 1 (first from 0507 kgm up to 1112 kgmand then from 1112 kgm up to 3168 kgm) As a result twosharp growths of the wipe rope tension loading on the rocketoccur and cause twomajor large-amplitude oscillations of thecurves just around the time 119905119908 shown in Figures 16ndash19 InTable 7 the 119905119908 moment fluctuates from 0197s to 0218s in sixtest runs

After observing the test photographs taken around 119905119908it is found out that the rocket exactly starts to pull outthe supporting bar of the first net unit at this momentwhich leads to the second jump of the pulled-out endingrsquoslinear density All four measured parameters go throughthe biggest oscillation and valuable engineering elementssuch as the maximum wire rope tension the maximumresultant velocity themaximum longitudinal velocity and themaximumhorizontal velocity of the rocket centroid (denotedas 119881119877max 119881119877119909maxand 119881119877119910max in Table 7) appear around 119905119908It is also worth mentioning that since the flying length ofthe net is relatively short in Phase 1 the waving behavior offlexible net belts is not remarkable enough to dominate thedynamic process The rocket flies under an intense dynamicloading condition due to sudden changes in longitudinallinear density of the pulled-out ending which is the reasonwhy time-variation curves in Figures 16ndash19 differ little inPhase 1

In Phase 1 it can be concluded that the simulation resultsacquire good accuracies in both predicting average behaviorsand catching oscillations of the measured parameters Com-pared with all six runs the error rates of average values infour essential dynamic parameters are -105sim-82 -144sim

-120 +104sim+128 and -209sim-179 (seen in Tables8ndash11) Meanwhile simulation curves exhibit the similar high-frequency and large-amplitude oscillations and perform wellin reproducing the overall changing trends and frequency ofthe oscillations As can be seen in Figures 16ndash19 the modelis able to predict the occurring time of the maximum wirerope tension (119905119908) and three other key engineering elements(119881119877max 119881119877119909max and 119881119877119910max) as approximate engineeringestimatesThe error ranges are -0024sim-0003s -594sim-11ms-914sim-412ms and +277sim+471ms respectively Figure 20indicates the wire rope tension curve in simulation Thechanging frequency of tension value stays at an extremelyhigh level It can be inferred that the model manages topredict the two sharp growths of the wire rope tensionemerging around 119905119908 in Phase 1 Maximum instantaneousvalue of the tension reaches over 10KN which is aboutten times the value of the rocket thrust With such a highfrequency and large amplitudes in its oscillations the wirerope tension becomes a fundamental element for the flightstability since it determines the moment imposed on therocket

Phase 2 is characterized from 1199051 = 05119904 to 1199052 = 18119904where 1199052 = 18119904 represents the moment in which the rocketstops working The net is pulled out of the container unit byunit and flies at a waving status Longitudinal linear density ofthe pulled-out ending no longer jumps due to the more evendensity of the net Consequently due to the waving behaviorof flexible net belts the constant stress waves spread throughthe net and the wire rope and become the second majordisturbance on the attitude and velocity of the rocket exceptfor its own thrust Since the stress waves are much slighterthan the strong impact process in Phase 1 the amplitudes of


the oscillations in Figures 16ndash19 all undergo a big drop and thedynamic parameters fluctuate around steady average valuesin Phase 2

Compared with test results in Phase 2 the model curvesexhibit medium-amplitude oscillations around similar aver-age values which means that the model is still able to predictthe overall kinetic energy of the system in high precisionTheerror rates of average values in four essential dynamic param-eters are +22sim+42 +01sim+23 +106sim+144 and-32sim-08 (seen in Tables 8ndash11)

However the model fails to describe the changing trendsof the oscillations and the amplitudes of the oscillationsare larger than test runs These disagreements are alsocaused by deficiencies of the tension modelmentioned aboveAlthough the elastic hysteresis of woven fabrics in net belts isconsidered in this work by introducing a hysteresis coefficientwhen correcting the linear elastic model applied in previousresearch [23] there is still room for improvement of themodified tensionmodel especially in characterizing the stressin net belts during the unloading cycle As can be inferredin Figure 6 after three loading-unloading cycles when thenet belt contracts below 13 of the maximum strain in thethird cycle the corresponding stress falls down to 110 ofthe maximum stress However the modified tension modelstill remains a relatively higher stress under the unloadingcircumstance The eccentric higher restoring force of themodel that occurred in the contracting stage of net belts is themain factor causing the larger amplitudes of the oscillationsin simulation

Phase 3 is characterized from 1199052 = 18119904 to 1199053 = 254119904where 1199053 represents the time when the retaining rope startsfunctioning as a buffer The rocket stops working and thewhole system enters into a free flight phase during this periodSince the rocket thrust is no longer imposed as a strongdriving force the oscillations of the dynamic parametersbegin to decay The aerodynamic force is no more ignorableand becomes the major factor in maintaining the constantwaving action of the system Accordingly the amplitudes ofthe oscillations in all test phenomena continue to decrease

The model is simplified under several assumptionsaerodynamic force is ignored when establishing the modelInstead of a constantly damping swing-motion appearing inthe flight test the rocket in simulation reaches at a stablegliding state without any oscillation right after its extinctionThemodel curves can no more exhibit oscillations Howeverit still functions well in predicting the overall kinetic energyof the system with acceptable deviation of average values infour essential dynamic parameters The corresponding errorranges are -13sim+03 -86sim-64 +14sim+25 and -302sim-244 (seen in Tables 8ndash11)

Phase 4 is characterized from 1199053 to the end of the flightwhen the rocket lands on the ground As stated above theunusual large stiffness of the tension model in this workmagnifies the buffer action of the retaining rope and causesthe eccentric ballistic reverse in the numerical example Soa fully description distortion of the model appears in thisphase Comparisons between flight tests and simulation inPhase 4 are no more necessary and are not included inTables 8ndash11

Through the phase-by-phase oscillation analysis statedabove the agreement between simulation results of themodeland flight tests is fully evaluated Firstly during the mainpart (0sim254s as Phases 1sim3) of RTNS movement the sim-ulation results acquire a good accuracy in describing averagebehaviors of the measured parameters with acceptable errorrates which indicates the capability of themodel in predictingthe overall kinetic energy of the system Furthermore themodel performs well in catching the high-frequency andlarge-amplitude oscillations in the intense dynamic loadingphase (0sim05s as Phase 1) Combining the discussion onoscillation analysis with the ballistic curve comparison it canbe concluded that the model succeeds in predicting severalkey engineering elements including119879119891119883max119884max 119905119908119881119877max119881119877119909max and 119881119877119910max

Taken altogether the multibody model established in thiswork functions well as a qualified theoretical guidance forexperimental design and achieves the goals on predictingessential engineering factors during the RTNS deployingprocess as an approximate engineering reference It appearsto be a referential model with potential applications forthe future modifying of RTNS As an example for futureRTNS prototypes designed with different distributions oflongitudinal linear density themodel is able to predict almostthe exact time points when the sharp growths of the wire ropetension emerge in Phase 1 for each prototype The numericalintense-loading times will be a valuable guidance for activecontrol scheme on the rocket Moreover the numericalmaximumwire rope tension is also an instruction for strengthcheck of the supporting bars

Furthermore a time correlation analysis based on corre-lation coefficients between time-variation curves in Figures16ndash19 is fulfilled to assess the agreements between simulationand flight tests from a statistical point of view Firstly thefirst six columns in Tables 3ndash6 indicate the correlationsbetween experimental data of different runs Almost allcorrelation coefficients between measured values of the sameparameter in six runs stay at the scope of 08sim09 whichproves a high consistency in test phenomena Secondlydivergences between the correlation coefficients in the lasttwo columns also separate the ending phase of the ballisticsimulation which has a clear disagreement with the testsdue to deficiencies existing in the tension model fromPhase 1 to 3 of RTNS movement Comparing simulationresults with six runs in Phases 1sim3 correlation coefficientsbetween resultant velocities of the rocket centroid longitu-dinal velocities of the rocker centroid horizontal velocitiesof the rocket centroid and rocket pitching angles fluctuateat 06975sim07415 07170sim07824 07542sim07722 and 06008sim06160 respectively Therefore significant correlations arefound between test data and simulation results which provesthat the model statistically matches the flight tests well

7 Conclusions and Future Work

In present study a lumpedmass multibody model of RTNS isestablished by the Cartesian coordinate method After modi-fying the model by introducing the elastic hysteresis of woven


fabrics and setting up the initial state computer codes are self-programmed and numerical simulations are accomplished inMATLAB Furthermore we design a RTNS prototype andconduct six flight tests in a shooting range With a goodconsistency of the essential engineering factors the prototypemanages to function well and meet the engineering aims inthe deploying process Inconsistent thrust curves betweendifferent rockets in the initial trajectory and aerodynamicforce in the ending phase are two main factors causing thefluctuation between test data of six runs according to theexperimental fluctuation analysis

Comparison of ballistic curves is finished The ballisticsimulation matches the test ballistics well with small errorranges (all within 10) in flight time ballistic peak point andshooting range

In order to carry out a further investigation on the numer-ical performance of the multibody model four essentialdynamic parameters including the rocket pitching angle theresultant velocity the horizontal velocity and the longitu-dinal velocity of the rocket centroid are studied by usingcomparative analysis between simulation results and testdata The RTNS operation is divided into four particularphases based upon different levels of agreements on the time-variation curves between simulation and tests A phase-by-phase oscillation analysis is fulfilled while both accuraciesin predicting average behaviors and catching oscillationsof the measured parameters are taken into considerationMeanwhile with several characteristic times (119905119908 1199051 1199052 and 1199053)defined in four phases connections between the oscillationsin simulation and real test phenomena are studied

During the main part (0sim254s as Phases 1sim3) of theflight the simulation results acquire a good accuracy indescribing average behaviors of the measured parameterswith acceptable error rates (within 15mostly in Tables 8ndash11)which indicates the capability of the model in predictingthe overall kinetic energy of the system Furthermore themodel achieves the goals on catching the high-frequency andlarge-amplitude oscillations in the intense dynamic loadingphase (0sim05s as Phase 1) Several key engineering elements(including the maximum resultant velocity the maximumlongitudinal velocity and the maximum horizontal velocityof the rocket centroid the maximum wire rope tension andits occurring time) emerging in this phase are successfullypredicted by the simulation results with small fluctuationsbetween the tests (shown in Table 7) which signifies that themultibody model proposed in this work functions well as aqualified theoretical guidance for experimental design andachieves in predicting essential engineering factors duringthe RTNS deploying process as an approximate engineeringreference The multibody model appears to be a referentialtool with potential applications for the future modifying ofRTNS

Furthermore a time correlation analysis based on cor-relation coefficients between simulation and test curves isconducted Significant correlations are found between testdata and simulation results which proves that the modelstatistically matches the flight tests well

However there are few deficiencies existing in themultibody model which lead to the simulation errors The

model curves fail to exhibit oscillations in Phase 3 due toits neglection of aerodynamic force The eccentric higherrestoring force in the model that occurred at the contractingstage of net remains unsolved which is the main cause forlarger numerical amplitudes of the oscillations in Phase 2 andthe full description distortion in Phase 4These issues shouldbe considered in future research to modify the multibodymodel

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Methodology was done by Qiao Zhou and Feng Hannumerical validation was made by Qiao Zhou and FengHan flight test was made by Qiao Zhou and Fang Chendata accuracy was done by Qiao Zhou and Fang Chenwritingmdashoriginal draft preparationmdash was achieved by QiaoZhou writingmdashreview and editingmdashwas achieved by QiaoZhou Fang Chen and Feng Han project administration wasdone by Feng Han funding acquisition was got by Feng Hanand Fang Chen

Acknowledgments

This research was funded by the National Natural ScienceFoundation of China Grant number 3020020121137

References

[1] WGuM Lu J LiuQDong ZWang and J Chen ldquoSimulationand experimental research on line throwing rocket with flightrdquoDefence Technology vol 10 no 2 pp 149ndash153 2014

[2] M Lu G Wenbin L Jianqing W Zhenxiong and X JinlingldquoDynamic modeling of the line throwing rocket with flightmotion based on kanersquos methodrdquo Journal of Mechanics vol 22no 5 pp 401ndash409 2016

[3] M Frank L H Richards P L Mcduffie C Kohl and T GRatliff Method for breaching a minefield United States Patent8037797 2011 httpwwwfreepatentsonlinecom8037797pdf

[4] A Ionel ldquoNumerical study of rocket upper stage deorbitingusing passive electrodynamic tether dragrdquo INCAS BULLETINvol 6 no 4 pp 51ndash61 2014

[5] S Djerassi and H Bamberger ldquoSimultaneous deployment of acable from twomoving platformsrdquo Journal of Guidance Controland Dynamics vol 21 no 2 pp 271ndash276 1998

[6] K K Mankala and S K Agrawal ldquoDynamic modeling andsimulation of impact in tether netgripper systemsrdquo MultibodySystem Dynamics vol 11 no 3 pp 235ndash250 2004

[7] PWilliams and P Trivailo ldquoDynamics of circularly towed aerialcable systems part i optimal configurations and their stabilityrdquo


Journal of Guidance Control and Dynamics vol 30 no 3 pp753ndash765 2007

[8] P Williams and P Trivailo ldquoDynamics of circularly towedaerial cable systems part 2 transitional flight and deploymentcontrolrdquo Journal of Guidance Control and Dynamics vol 30no 3 pp 766ndash779 2007

[9] P Trivailo D Sgarioto and C Blanksby ldquoOptimal control ofaerial tethers for payload rendezvousrdquo in Proceedings of theControl Conference 2004

[10] P Williams D Sgarioto and P Trivailo ldquoOptimal control ofan aircraft-towed flexible cable systemrdquo Journal of GuidanceControl and Dynamics vol 29 no 2 pp 401ndash410 2006

[11] P Williams ldquoOptimal terrain-following for towed-aerial-cablesensorsrdquoMultibody SystemDynamics vol 16 no 4 pp 351ndash3742006

[12] P Williams ldquoDynamic multibody modeling for tethered spaceelevatorsrdquoActaAstronautica vol 65 no 3-4 pp 399ndash422 2009

[13] P M Trivailo and H Kojima ldquoDynamics of the net systemscapturing space debrisrdquo Transactions of the Japan Society forAeronautical and Space Sciences Aerospace Technology Japanvol 14 pp 57ndash66 2016

[14] I Sharf BThomsen EM Botta andAKMisra ldquoExperimentsand simulation of a net closing mechanism for tether-netcapture of space debrisrdquoActaAstronautica vol 139 pp 332ndash3432017

[15] B Buckham and M Nahon ldquoDynamics simulation of lowtension tethersrdquo in Proceedings of the Oceans rsquo99 MTSIEEERiding the Crest into the 21st Century Conference and Exhibitionpp 757ndash766 Seattle WA USA 1999

[16] B Buckham M Nahon M Seto X Zhao and C LambertldquoDynamics and control of a towed underwater vehicle systempart I model developmentrdquo Ocean Engineering vol 30 no 4pp 453ndash470 2003

[17] C Lambert M Nahon B Buckham and M Seto ldquoDynamicsand control of towed underwater vehicle system part II modelvalidation and turn maneuver optimizationrdquo Ocean Engineer-ing vol 30 no 4 pp 471ndash485 2003

[18] S Prabhakar and B Buckham ldquoDynamics modeling and con-trol of a variable length remotely operated vehicle tetherrdquo inPro-ceedings of the OCEANS 2005 MTSIEEE pp 1ndash8 WashingtonDC USA 2005

[19] T Takagi T Shimizu K Suzuki T Hiraishi and K YamamotoldquoValidity and layout of ldquoNaLArdquo a net configuration and loadinganalysis systemrdquo Fisheries Research vol 66 no 2-3 pp 235ndash2432004

[20] T Shimizu T Takagi H Korte T Hiraishi and K YamamotoldquoApplication of NaLA a fishing net configuration and loadinganalysis system to drift gill netsrdquo Fisheries Research vol 76 no1 pp 67ndash80 2005

[21] T Shimizu T Takagi H Korte T Hiraishi and K YamamotoldquoApplication of NaLA a fishing net configuration and loadinganalysis system to bottom gill netsrdquo Fisheries Science vol 73no 3 pp 489ndash499 2007

[22] K Suzuki T Takagi T Shimizu T Hiraishi K Yamamotoand K Nashimoto ldquoValidity and visualization of a numericalmodel used to determine dynamic configurations of fishingnetsrdquo Fisheries Science vol 69 no 4 pp 695ndash705 2003

[23] F Han H Chen and Q Zhu ldquoModelling and simulation ofa rocket-towed net systemrdquo International Journal of ModellingIdentification and Control vol 20 no 3 p 279 2013

[24] S Jian H Feng C Fang Z Qiao and PM Trivailo ldquoDynamicsand modeling of rocket towed net systemrdquo Proceedings of theInstitution of Mechanical Engineers Part G Journal of AerospaceEngineering vol 232 no 1 pp 185ndash197 2016

[25] A A Shabana Computational Dynamics Wiley West SussexUK 3rd edition 2010

[26] A A Shabana Dynamics of Multibody Systems CambridgeUniversity Press New York NY USA 2005

[27] E H Taibi AHammouche and A Kifani ldquoModel of the tensilestress-strain behavior of fabricsrdquo Textile Research Journal vol71 no 7 pp 582ndash586 2016

[28] R Foroutan J Nemes H Ghiasi and P Hubert ldquoExperimentalinvestigation of high strain-rate behaviour of fabric compos-itesrdquo Composite Structures vol 106 pp 264ndash269 2013

[29] P Ma H Hu L Zhu B Sun and B Gu ldquoTensile behaviors ofco-woven-knitted fabric reinforced composites under variousstrain ratesrdquo Journal of Composite Materials vol 45 no 24 pp2495ndash2506 2011

[30] B Bridgens and M Birchall ldquoForm and function the signif-icance of material properties in the design of tensile fabricstructuresrdquo Engineering Structures vol 44 pp 1ndash12 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


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Applied MathematicsJournal of


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International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


are two mainstream modeling approaches adopted in theo-retical research and engineering applications Although thecontinuum method is considered to be more accurate themultibody theory represented by the lumped mass methodan emerging methodology in the research field of dynamiccharacteristics of flexible cablenet is more compatible tobe applied to complex multibody dynamics and computerprogramming Many other scholars continued applying anddeveloping lumped mass method in aerospace engineering[7ndash14] and ocean engineering fields [15ndash22]

Williams and Trivailo [7 8] studied the dynamics of acircling aircraft-towed cable system A lumped mass modelof the cable was built for the circularly towed configurationpractical towing solutions that achieve small motion of thetowed body were obtained by using constrained numeri-cal optimization Meanwhile they studied the transitionaldynamics as the aircraft changes from straight flight tocircular flight by assuming no tension in the cable Williamslead his team [9ndash12] in investigating the dynamic deploymentof aircraft-towed cable dropping systems They proposed azero-tension cable model by using lumped masses connectedvia rigid links and modified it by introducing the linearelastic tension hypothesis Then aerodynamic force actingupon the discrete links was considered when simulatingthe flight attitude of the cable and optimal control schemeswere presented through a parameterization study on essentialcontrol variables Trivailo and Kojima [13] developed thecomprehensive nonlinear models of following net capturingsystems for debris removal Dynamics of the net systemsand their interaction with the capturing objects were studiedSharf et al [14] presented a concept for a net closingmechanism they finished the design and testing of a debriscontainment system for use in a tether-net approach to spacedebris removal

Buckham et al [15ndash18] adopted a mass-spring model toreveal the dynamic behavior of the cable in a towed underwa-ter vehicle system by taking into account the cable viscosityFurthermore they introduced the flexural rigidity of thecable into the previous proposed model following GalerkinPrinciple Bending moment acting on the cable segment wastransformed to concentrated force imposed on the discretemass in order to increase the model accuracy in describingthe attitude of the cable under low-tension situations TakagiT et al [19ndash22] developed a net-configuration and load-analysis system under ocean current effect based on a mass-spring model

In this paper a lump-mass multibody model of RTNS isestablished by the Cartesian coordinate method in the case ofa two-dimensional assumption This model is involved in theelasticity of the wire rope flexible mesh-belts and retainingrope Due to the complex operating conditions we finishthe calculation of the initial RTNS position when the net isarranged in its container before launching By taking intoaccount the elastic hysteresis of woven fabrics we proposeda modified tension model of mesh-belts Furthermore aprototype of RTNS is designed and built Flight tests areconducted in a shooting range Ballistic curves and fouressential dynamic parameters are studied by using compar-ative analysis between simulation results and test data The

6 5 4 3 2

1

7

Figure 1 Rocket-towed net system 1 rocket 2 wire rope 3transition section 4 net 5 supporting bar 6 net container 7launching platform

simulation acquires a good accuracy in describing averagebehaviors of the measured parameters with acceptable errorrates in the main part of the flight and manages to catch theoscillations in the intense dynamic loading phase

2 Multibody Model

21 Deployment Process of RTNS As shown in Figure 1 RTNSis a quite complex set of devices It consists of a rocket anet part a launching platform (including a tractor and a netcontainer) and connecting devices (including awire rope anda retaining rope) between them

During the working process of RTNS the launching plat-form and the net container are almost stationary Thereforeas shown in Figure 2 the major research targets of RTNS arethe net the rocket and the connecting devices

As shown in Figure 2 the flexible fabric net is made ofsix net units and two transition sections Each unit contains4 longitudinal mesh-belts and 24 transverse mesh-beltsTwo transition sections refer to the front and back mesh-belts which connect the six units to the wire rope and theretaining rope The mesh-belts are woven from nylon Inevery longitudinal-transverse intersection there is a screwwhich connects the belts in orthogonal directions In orderto keep the net stretching out and tight longitudinally sevenequidistant transverse supporting bars are set at the frontback and middle of the net The bars link six net unitstogether Two ends of the net are connected to the rocketand the fixing device by the wire rope and the retaining roperespectively

The launching-flying-landing deployment process ofRTNS can be divided into four phases as follows

(1) The rocket is launched from the platform and startspulling the wire rope connecting behind it

(2) The net begins being towed out of the container unitby unit until the rocket engine finishes working

(3) RTNS continues flying forward with inertia until theretaining rope starts functioning


1234567

6000mm

1000mm

30800mm1000mm

4800mm

3000mm


Tran

sver

se d

irecti

on


12345678
























Y

X

O

Mi (xi yi)

M1 (x1 y1)

C (x0 y0)

P (xd yd)

0

Force element



q = [119909119889 119910119889 1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873]119879 (1)

3 Dynamic Equations


q = [1199021 1199022 sdot sdot sdot 119902119899]119879 (2)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 0 (3)


119876119890119898 + 119876119868119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (4)


119862119894 (q 119905) = 0 (119894 = 1 2 sdot sdot sdot 119904) (5)



119899sum119898=1

120597119862119894120597119902119898 120575119902119898 = 0 119894 = 1 2 sdot sdot sdot 119904 (6)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 119904sum119894=1

(120582119894 119899sum119898=1

120597119862119894120597119902119898 120575119902119898)

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 minus 119899sum119898=1

119904sum119894=1

120582119894 120597119862119894120597119902119898 120575119902119898 = 0

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898)120575119902119898 = 0

(7)


119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (8)



119876119890119898 + 119876119868119898 minus 119904sum119894=1


(9)






Mq + Cq119879120582 = F




F

= [119865119889119909 119865119889119910 1198720 1198650119909 1198650119910 1198651119909 1198651119910 sdot sdot sdot 119865119899119909 119865119899119910]119879 (14)


F0 = [1198650119909 1198650119910]119879 = F119903 + G0 (15)


F119894 = [119865119894119909 119865119894119910]119879 = G119894 + T119894 minus T119894+1



F119889 = [119865119889119909 119865119889119910]119879 = G119889 minus T1 (17)

F119899 = [119865119899119909 119865119899119910]119879 = G119889 + T119899 (18)






q = [q119889 q119894]119879 (19)

Cq = [Cq119889 Cq119894] (20)


q119889 = [119909119889 119910119889] (21)

q119894 = [1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873] (22)

Cq119889 = [minus1 00 minus1] (23)



Cq119889q119889 + Cq119894q119894 + C119905 = 0 (25)



120573 = (Cqq)q q = [[021198970 cos 1205790021198970 sin 1205790

]]

(27)



minus1120573 = Cq119894q119894 + 120573 (28)


q = Aq119894 + b (29)

where

A = [Cq119894

I] (30)

b = [1205730] (31)


M (Aq119894 + b) + Cq119879120582 = F (32)


M = [M119889 00 M119894

] (33)

F = [F119889F119894

] (34)


(Cq119894119879M119889Cq119894 + M119894) q119894 = F119894 + Cq119894

119879F119889 + Cq119894119879M119889120573 (35)







F119903 = 119865 (119905) sdot n (1205790) (36)


n (1205790) = [cos 1205790 sin 1205790]119879 (37)


119897119894 = 1003816100381610038161003816riminus1 minus r1198941003816100381610038161003816 (38)


(a) (b)




119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)





400

300

200

100

0

Stre

ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N






(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=24s

(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)



Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)












40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(b) Run 2

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(d) Run 4

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(e) Run 5

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(f) Run 6






403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(a) Run 1

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

Ｎ2 Ｎ3

ＮＱ

Ｎ1

(b) Run 2

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

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12000

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rope

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ion

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time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









1234567

6000mm

1000mm

30800mm1000mm

4800mm

3000mm


Tran

sver

se d

irecti

on


12345678
























Y

X

O

Mi (xi yi)

M1 (x1 y1)

C (x0 y0)

P (xd yd)

0

Force element



q = [119909119889 119910119889 1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873]119879 (1)

3 Dynamic Equations


q = [1199021 1199022 sdot sdot sdot 119902119899]119879 (2)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 0 (3)


119876119890119898 + 119876119868119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (4)


119862119894 (q 119905) = 0 (119894 = 1 2 sdot sdot sdot 119904) (5)



119899sum119898=1

120597119862119894120597119902119898 120575119902119898 = 0 119894 = 1 2 sdot sdot sdot 119904 (6)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 119904sum119894=1

(120582119894 119899sum119898=1

120597119862119894120597119902119898 120575119902119898)

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 minus 119899sum119898=1

119904sum119894=1

120582119894 120597119862119894120597119902119898 120575119902119898 = 0

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898)120575119902119898 = 0

(7)


119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (8)



119876119890119898 + 119876119868119898 minus 119904sum119894=1


(9)






Mq + Cq119879120582 = F




F

= [119865119889119909 119865119889119910 1198720 1198650119909 1198650119910 1198651119909 1198651119910 sdot sdot sdot 119865119899119909 119865119899119910]119879 (14)


F0 = [1198650119909 1198650119910]119879 = F119903 + G0 (15)


F119894 = [119865119894119909 119865119894119910]119879 = G119894 + T119894 minus T119894+1



F119889 = [119865119889119909 119865119889119910]119879 = G119889 minus T1 (17)

F119899 = [119865119899119909 119865119899119910]119879 = G119889 + T119899 (18)






q = [q119889 q119894]119879 (19)

Cq = [Cq119889 Cq119894] (20)


q119889 = [119909119889 119910119889] (21)

q119894 = [1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873] (22)

Cq119889 = [minus1 00 minus1] (23)



Cq119889q119889 + Cq119894q119894 + C119905 = 0 (25)



120573 = (Cqq)q q = [[021198970 cos 1205790021198970 sin 1205790

]]

(27)



minus1120573 = Cq119894q119894 + 120573 (28)


q = Aq119894 + b (29)

where

A = [Cq119894

I] (30)

b = [1205730] (31)


M (Aq119894 + b) + Cq119879120582 = F (32)


M = [M119889 00 M119894

] (33)

F = [F119889F119894

] (34)


(Cq119894119879M119889Cq119894 + M119894) q119894 = F119894 + Cq119894

119879F119889 + Cq119894119879M119889120573 (35)







F119903 = 119865 (119905) sdot n (1205790) (36)


n (1205790) = [cos 1205790 sin 1205790]119879 (37)


119897119894 = 1003816100381610038161003816riminus1 minus r1198941003816100381610038161003816 (38)


(a) (b)




119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)





400

300

200

100

0

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ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N






(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



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Figure 13 RTNS test





6 Discussion




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12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018



















Y

X

O

Mi (xi yi)

M1 (x1 y1)

C (x0 y0)

P (xd yd)

0

Force element



q = [119909119889 119910119889 1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873]119879 (1)

3 Dynamic Equations


q = [1199021 1199022 sdot sdot sdot 119902119899]119879 (2)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 0 (3)


119876119890119898 + 119876119868119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (4)


119862119894 (q 119905) = 0 (119894 = 1 2 sdot sdot sdot 119904) (5)



119899sum119898=1

120597119862119894120597119902119898 120575119902119898 = 0 119894 = 1 2 sdot sdot sdot 119904 (6)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 119904sum119894=1

(120582119894 119899sum119898=1

120597119862119894120597119902119898 120575119902119898)

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 minus 119899sum119898=1

119904sum119894=1

120582119894 120597119862119894120597119902119898 120575119902119898 = 0

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898)120575119902119898 = 0

(7)


119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (8)



119876119890119898 + 119876119868119898 minus 119904sum119894=1


(9)






Mq + Cq119879120582 = F




F

= [119865119889119909 119865119889119910 1198720 1198650119909 1198650119910 1198651119909 1198651119910 sdot sdot sdot 119865119899119909 119865119899119910]119879 (14)


F0 = [1198650119909 1198650119910]119879 = F119903 + G0 (15)


F119894 = [119865119894119909 119865119894119910]119879 = G119894 + T119894 minus T119894+1



F119889 = [119865119889119909 119865119889119910]119879 = G119889 minus T1 (17)

F119899 = [119865119899119909 119865119899119910]119879 = G119889 + T119899 (18)






q = [q119889 q119894]119879 (19)

Cq = [Cq119889 Cq119894] (20)


q119889 = [119909119889 119910119889] (21)

q119894 = [1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873] (22)

Cq119889 = [minus1 00 minus1] (23)



Cq119889q119889 + Cq119894q119894 + C119905 = 0 (25)



120573 = (Cqq)q q = [[021198970 cos 1205790021198970 sin 1205790

]]

(27)



minus1120573 = Cq119894q119894 + 120573 (28)


q = Aq119894 + b (29)

where

A = [Cq119894

I] (30)

b = [1205730] (31)


M (Aq119894 + b) + Cq119879120582 = F (32)


M = [M119889 00 M119894

] (33)

F = [F119889F119894

] (34)


(Cq119894119879M119889Cq119894 + M119894) q119894 = F119894 + Cq119894

119879F119889 + Cq119894119879M119889120573 (35)







F119903 = 119865 (119905) sdot n (1205790) (36)


n (1205790) = [cos 1205790 sin 1205790]119879 (37)


119897119894 = 1003816100381610038161003816riminus1 minus r1198941003816100381610038161003816 (38)


(a) (b)




119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)





400

300

200

100

0

Stre

ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N






(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

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4

2

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)

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(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

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7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

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12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018










119899sum119898=1

120597119862119894120597119902119898 120575119902119898 = 0 119894 = 1 2 sdot sdot sdot 119904 (6)


119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 = 119904sum119894=1

(120582119894 119899sum119898=1

120597119862119894120597119902119898 120575119902119898)

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898) 120575119902119898 minus 119899sum119898=1

119904sum119894=1

120582119894 120597119862119894120597119902119898 120575119902119898 = 0

997904rArr 119899sum119898=1

(119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898)120575119902119898 = 0

(7)


119876119890119898 + 119876119868119898 minus 119904sum119894=1

120582119894 120597119862119894120597119902119898 = 0 (119898 = 1 2 sdot sdot sdot 119899) (8)



119876119890119898 + 119876119868119898 minus 119904sum119894=1


(9)






Mq + Cq119879120582 = F




F

= [119865119889119909 119865119889119910 1198720 1198650119909 1198650119910 1198651119909 1198651119910 sdot sdot sdot 119865119899119909 119865119899119910]119879 (14)


F0 = [1198650119909 1198650119910]119879 = F119903 + G0 (15)


F119894 = [119865119894119909 119865119894119910]119879 = G119894 + T119894 minus T119894+1



F119889 = [119865119889119909 119865119889119910]119879 = G119889 minus T1 (17)

F119899 = [119865119899119909 119865119899119910]119879 = G119889 + T119899 (18)






q = [q119889 q119894]119879 (19)

Cq = [Cq119889 Cq119894] (20)


q119889 = [119909119889 119910119889] (21)

q119894 = [1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873] (22)

Cq119889 = [minus1 00 minus1] (23)



Cq119889q119889 + Cq119894q119894 + C119905 = 0 (25)



120573 = (Cqq)q q = [[021198970 cos 1205790021198970 sin 1205790

]]

(27)



minus1120573 = Cq119894q119894 + 120573 (28)


q = Aq119894 + b (29)

where

A = [Cq119894

I] (30)

b = [1205730] (31)


M (Aq119894 + b) + Cq119879120582 = F (32)


M = [M119889 00 M119894

] (33)

F = [F119889F119894

] (34)


(Cq119894119879M119889Cq119894 + M119894) q119894 = F119894 + Cq119894

119879F119889 + Cq119894119879M119889120573 (35)







F119903 = 119865 (119905) sdot n (1205790) (36)


n (1205790) = [cos 1205790 sin 1205790]119879 (37)


119897119894 = 1003816100381610038161003816riminus1 minus r1198941003816100381610038161003816 (38)


(a) (b)




119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)





400

300

200

100

0

Stre

ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N






(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

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)

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time (s)

t=0s

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(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

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7100mm 7900mm

783

00m

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8400mm 8200mm

300

0m

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31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

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rock

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(f) Run 6











12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018












q = [q119889 q119894]119879 (19)

Cq = [Cq119889 Cq119894] (20)


q119889 = [119909119889 119910119889] (21)

q119894 = [1205790 1199090 1199100 sdot sdot sdot 119909119873 119910119873] (22)

Cq119889 = [minus1 00 minus1] (23)



Cq119889q119889 + Cq119894q119894 + C119905 = 0 (25)



120573 = (Cqq)q q = [[021198970 cos 1205790021198970 sin 1205790

]]

(27)



minus1120573 = Cq119894q119894 + 120573 (28)


q = Aq119894 + b (29)

where

A = [Cq119894

I] (30)

b = [1205730] (31)


M (Aq119894 + b) + Cq119879120582 = F (32)


M = [M119889 00 M119894

] (33)

F = [F119889F119894

] (34)


(Cq119894119879M119889Cq119894 + M119894) q119894 = F119894 + Cq119894

119879F119889 + Cq119894119879M119889120573 (35)







F119903 = 119865 (119905) sdot n (1205790) (36)


n (1205790) = [cos 1205790 sin 1205790]119879 (37)


119897119894 = 1003816100381610038161003816riminus1 minus r1198941003816100381610038161003816 (38)


(a) (b)




119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)





400

300

200

100

0

Stre

ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N






(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=24s

(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)



Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)












40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(b) Run 2

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(d) Run 4

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(e) Run 5

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(f) Run 6






403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(a) Run 1

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

Ｎ2 Ｎ3

ＮＱ

Ｎ1

(b) Run 2

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(d) Run 4

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(e) Run 5

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(f) Run 6







20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

Ｎ2Ｎ3

(a) Run 1

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱＮ1

Ｎ2Ｎ3

(b) Run 2

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱＮ1

Ｎ2Ｎ3

(c) Run 3

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱＮ1

Ｎ2Ｎ3

(d) Run 4

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱＮ1

Ｎ2Ｎ3

(e) Run 5

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱＮ1

Ｎ2Ｎ3

(f) Run 6







806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

Ｎ2 Ｎ3

rock

et p

itchi

ng an

gle (

∘ )

(a) Run 1

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 2Simulation

rock

et p

itchi

ng an

gle (

∘ )

(b) Run 2

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 3Simulation

rock

et p

itchi

ng an

gle (

∘ )

(c) Run 3

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 4Simulation

rock

et p

itchi

ng an

gle (

∘ )

(d) Run 4

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 5Simulation

rock

et p

itchi

ng an

gle (

∘ )

(e) Run 5

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 6Simulation

rock

et p

itchi

ng an

gle (

∘ )

(f) Run 6











12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b)




119879119894 = 119860 119894119864119894 119897119894 minus 119897119900119894119897119900119894 119897119894 ge 1198971199001198940 119897119894 lt 119897119900119894 (39)





400

300

200

100

0

Stre

ss (M

Pa)

000 001 002 003 004 005 006 007 008 009

Strain

3000 N5000 N7000 N






(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=24s

(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)



Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)












40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(b) Run 2

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(d) Run 4

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(e) Run 5

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(f) Run 6






403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(a) Run 1

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

Ｎ2 Ｎ3

ＮＱ

Ｎ1

(b) Run 2

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(d) Run 4

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(e) Run 5

403020100

minus10

long

itudi

nal v

eloci

ty o

fth

e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(f) Run 6







20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

Ｎ2Ｎ3

(a) Run 1

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱＮ1

Ｎ2Ｎ3

(b) Run 2

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱＮ1

Ｎ2Ｎ3

(c) Run 3

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱＮ1

Ｎ2Ｎ3

(d) Run 4

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱＮ1

Ｎ2Ｎ3

(e) Run 5

20

10

0

minus10

minus20

horiz

onta

l velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱＮ1

Ｎ2Ｎ3

(f) Run 6







806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

Ｎ2 Ｎ3

rock

et p

itchi

ng an

gle (

∘ )

(a) Run 1

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 2Simulation

rock

et p

itchi

ng an

gle (

∘ )

(b) Run 2

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 3Simulation

rock

et p

itchi

ng an

gle (

∘ )

(c) Run 3

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 4Simulation

rock

et p

itchi

ng an

gle (

∘ )

(d) Run 4

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 5Simulation

rock

et p

itchi

ng an

gle (

∘ )

(e) Run 5

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 6Simulation

rock

et p

itchi

ng an

gle (

∘ )

(f) Run 6











12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b)


bracing force

frictionforce

gravity



119879119894 =


(41)




G119894 = [0 minus119898119894119892]119879 (42)





transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=24s

(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)



Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)












40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(b) Run 2

40

30

20

10

0resu

ltant

velo

city

of

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ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

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Run 3Simulation

ＮＱ

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(c) Run 3

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0resu

ltant

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(ms

)

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(d) Run 4

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10

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ocke

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(ms

)

0 05 1 15 2 25 3

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Run 5Simulation

ＮＱ

Ｎ1

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(e) Run 5

40

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10

0resu

ltant

velo

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of

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ocke

t cen

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(ms

)

0 05 1 15 2 25 3

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Run 6Simulation

ＮＱ

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(f) Run 6






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s)

0 05 1 15 2 25 3

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long

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s)

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(b) Run 2

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(c) Run 3

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(e) Run 5

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(f) Run 6







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(ms

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(ms

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(ms

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(f) Run 6







806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

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rock

et p

itchi

ng an

gle (

∘ )

(a) Run 1

ＮＱＮ1

Ｎ2 Ｎ3

806040200

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0 05 1 15 2 25 3

time (s)

Run 2Simulation

rock

et p

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gle (

∘ )

(b) Run 2

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Run 3Simulation

rock

et p

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gle (

∘ )

(c) Run 3

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Ｎ2 Ｎ3

806040200

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Run 4Simulation

rock

et p

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gle (

∘ )

(d) Run 4

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rock

et p

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(e) Run 5

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rock

et p

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gle (

∘ )

(f) Run 6











12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









transition section


PC

Y

O X

supporting bar

wire rope




Mq + Cq119879120582 = F

119894 = 0119894 = 0119894 = 0119894 = 0

(43)








4 Simulation




5 Flight Test



10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

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y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

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0

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y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=24s

(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)



Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)












40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

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Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

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Ｎ2Ｎ3

(b) Run 2

40

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20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

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(c) Run 3

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

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(d) Run 4

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20

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0resu

ltant

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city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

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(e) Run 5

40

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20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

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Run 6Simulation

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(f) Run 6






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0 05 1 15 2 25 3

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(a) Run 1

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Ｎ1

(b) Run 2

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(c) Run 3

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0 05 1 15 2 25 3

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(d) Run 4

403020100

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long

itudi

nal v

eloci

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e roc

ket c

entro

id (m

s)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

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(e) Run 5

403020100

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long

itudi

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fth

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s)

0 05 1 15 2 25 3

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Run 6Simulation

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(f) Run 6







20

10

0

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horiz

onta

l velo

city

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the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

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(a) Run 1

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0

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onta

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ocke

t cen

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horiz

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onta

l velo

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(ms

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Run 6Simulation

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(f) Run 6







806040200

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0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

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rock

et p

itchi

ng an

gle (

∘ )

(a) Run 1

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 2Simulation

rock

et p

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ng an

gle (

∘ )

(b) Run 2

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 3Simulation

rock

et p

itchi

ng an

gle (

∘ )

(c) Run 3

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 4Simulation

rock

et p

itchi

ng an

gle (

∘ )

(d) Run 4

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 5Simulation

rock

et p

itchi

ng an

gle (

∘ )

(e) Run 5

ＮＱＮ1

Ｎ2 Ｎ3

806040200

minus20minus40

0 05 1 15 2 25 3

time (s)

Run 6Simulation

rock

et p

itchi

ng an

gle (

∘ )

(f) Run 6











12000

10000

8000

6000

4000

2000

0

00 05 10 15 20

wire

rope

tens

ion

(N)

time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=0s

(a) t=0s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=04s

(b) t=04s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=08s

(c) t=08s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=12s

(d) t=12s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=16s

(e) t=16s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=20s

(f) t=20s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=24s

(g) t=24s

10

8

6

4

2

0

minus2

y (m

)

minus5 0 5 10 15 20 25 30 35 40

time (s)

t=251s

(h) t=251s





(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




Run 1Run 2Run 3

Run 4Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

0

2

4

6

8

10

12

Y (m

)



Run 5Run 6

0 5 10 15 20 25 30 35 40

X (m)

Simulation

0

2

4

6

8

10

12

Y (m

)












40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(a) Run 1

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(b) Run 2

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱ

Ｎ1

Ｎ2 Ｎ3

(c) Run 3

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

ＮＱ

Ｎ1

Ｎ2Ｎ3

(d) Run 4

40

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10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

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Ｎ2Ｎ3

(e) Run 5

40

30

20

10

0resu

ltant

velo

city

of

the r

ocke

t cen

troid

(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

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(f) Run 6






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long

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(a) Run 1

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long

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time (s)

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Ｎ1

(b) Run 2

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long

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(c) Run 3

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s)

0 05 1 15 2 25 3

time (s)

Run 4Simulation

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(d) Run 4

403020100

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long

itudi

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ket c

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id (m

s)

0 05 1 15 2 25 3

time (s)

Run 5Simulation

ＮＱ

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(e) Run 5

403020100

minus10

long

itudi

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eloci

ty o

fth

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id (m

s)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱ

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(f) Run 6







20

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0

minus10

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horiz

onta

l velo

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of

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ocke

t cen

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(ms

)

0 05 1 15 2 25 3

time (s)

Run 1Simulation

ＮＱＮ1

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(a) Run 1

20

10

0

minus10

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horiz

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ocke

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(ms

)

0 05 1 15 2 25 3

time (s)

Run 2Simulation

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0

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horiz

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(ms

)

0 05 1 15 2 25 3

time (s)

Run 3Simulation

ＮＱＮ1

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(c) Run 3

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horiz

onta

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(ms

)

0 05 1 15 2 25 3

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Run 4Simulation

ＮＱＮ1

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(d) Run 4

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0

minus10

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horiz

onta

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of

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(ms

)

0 05 1 15 2 25 3

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Run 5Simulation

ＮＱＮ1

Ｎ2Ｎ3

(e) Run 5

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0

minus10

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horiz

onta

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of

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ocke

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(ms

)

0 05 1 15 2 25 3

time (s)

Run 6Simulation

ＮＱＮ1

Ｎ2Ｎ3

(f) Run 6







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Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









(a) (b) (c)


1 2 3 4

5

6800mm

8800mm

6300mm

2000mm

7100mm 7900mm

783

00m

m

8400mm 8200mm

300

0m

m

31∘











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




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Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018











(a) t=0s (b) t=04s

(c) t=08s (d) t=12s

(e) t=16s (f) t=20s

(g) t=24s (h) t=251s

Figure 13 RTNS test





6 Discussion




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12000

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wire

rope

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ion

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time (s)



























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018









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Journal of







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Volume 2018









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Journal of












Journal of







Volume 2018






Volume 2018









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Journal of












Journal of







Volume 2018






Volume 2018











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wire

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Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018




























Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018
















Data Availability






Acknowledgments


References








































Journal of












Journal of







Volume 2018






Volume 2018








































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

Dynamic Modeling, Simulation, and Flight Test of a Rocket