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Formulas y demostracion de traslacion de ejes(Dinamica)
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Z
Y
X
J C
B
A
I
D
E
H F
G
No. a b c V x y z
1 30 35 30 31500 -15 17.5 -152 60 70 90 378000 -60 35 -453 18 20 25 9000 -21 45 -77.54 25 30 45 33750 -77.5 -15 22.55 10 10 20 2000 -57 60 10
454250
IXX IXY IXZ
I = IXY IYY IYZ
IXZ IYZ IZZ
Coordenas delcentro de masa
Momentos de Inercia al OrigenIxx Iyy Izz Ixy Ixz Iyz IXX
5578125 4725000 5578125 0 0 0 223125004.1E+08 368550000 2.68E+08 0 0 0 1638000000768750 711750 543000 0 0 0 73050000
8226563 7453125 4289063 0 0 0 3290625083333.33 83333.33333 33333.33 0 0 0 7483333.3333
1773752083
1773752083 9.67E+08 -7.63E+08
= 966987187.5 2.81E+09 -6.45E+08
-762823125 -6.45E+08 2.36E+09
Momentos de Inercia Ejes centro de masa
Productos de Inercia Ejes centro de masa
V(b2+c2)/12 V(a2+c2)/12 V(a2+b2)/12 IXX= Ixx+V dXx2
Momentos de Inercia al Origen Productos de Inercia al OrigenIYY IZZ IXY IXZ IYZ
IXY= Ixy+V dx dyIXZ= Ixz+V dx dzIYZ= Iyz+V dy dz
18900000 22312500 -8268750 7087500 -826875024948000002091600000 1.021E+09-793800000 -6E+08
58737000 22737000 14647500 -8505000 -31387500227250000 214593750 -58851563 39234375 -11390625
6781333.33 13731333 -1140000 -6840000 120000028064683332364974583 9.67E+08 -7.63E+08 -6E+08
IYY= Iyy+V dYy2 IZZ= Izz+V dZz2
Z
X`
CALCULAR LA INERCIA AL EJE AE
Z`
X 30 X`
H
g
E
FG
A
B
J C
I
ab
CALCULAR LA INERCIA AL EJE AEx y z
CoordenadasA 0 0 0
E -65 115 -90
Y rAE= -65 i 115 j -90 k
rAE= 159.84
uAE i cos B j k
Y`uAB= -0.38 i 0.768 j 0.512 k
tabla de cosenos directores
x y z
x' 0.768 -0.38 0.512
y' 0.512 0.768 -0.38
z' -0.38 0.512 0.768
cos a cos ƴ
B
D
E
I
-0.3841106 -0.3841106 1773752083 + -0.3841106 0.76822128 966987188
IAE= 0.76822128 -0.3841106 966987188 + 0.76822128 0.76822128 2806468333
0.51214752 -0.3841106 -762823125 + 0.51214752 0.76822128 -645196875
261701127 -285340482 150063566 ### ### ###
IAE= -285340482 1656276393 -253847951 ### ### ###
150063566 -253847951 620321202 ### ### ###
detAE= 2.5201E+26 ### ###
detAE= ###
1.77E+09 9.67E+08 -7.63E+08
l= 9.67E+08 2.81E+09 -6.45E+08
-7.63E+08 -6.45E+08 2.36E+09
966987188 + -0.38411063979869 0.512147519731584 -762823125
2806468333 + 0.768221279597376 0.512147519731584 -645196875
-645196875 + 0.512147519731584 0.512147519731584 2364974583.33333
