SIMULATION OF THE AIRBORNE PHASE OF THE GRAND JETÉ IN BALLET

D. Gordon E. Robertson, PhD, FCSB

Pamela Galler, BSc

Lisa Stanley, BSc

Biomechanics Laboratory,

School of Human Kinetics,

University of Ottawa, Ottawa, CANADA

Introduction

• Grand jeté is one of the strongest jumps in ballet

• It is characterized by a leap that travels horizontally

• Laws (2002) proposed that it is possible for the upper body to appear to translate in flight while the centre of gravity follows its parabolic path

Grand Jeté

Methods

• Two experienced ballet dancers/instructors

• Performed several grand jetés in sequence with a step in between jumps

• Some trials were done landing on a force platform

• Video taped at 60 fps

• 10-segment model of body (i.e., hands and feet ignored)

• Planar motion analysis

Methods

• Takeoff velocity determined from data preceding and after takeoff

• Initial estimate of total body angular momentum taken from average of flight phase momenta

• Joint displacements, initial position at takeoff, initial velocity and angular momentum were then used to iteratively obtain changes in trunk angle during flight (Lemaire & Robertson 1990)

• Total body angular momentum was adjusted by comparing simulated motion with actual motion

Methods

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Methods

• Once a successful simulation was achieved:

1. Hip joint displacements were modified to elevate lower extremities to produce full “split” in the air prior to reaching peak height

2. Shoulder joint displacements were then modified to raise the upper extremities until a “flat” trajectory of the head and shoulders was achieved

Results

• Neither dancer had a flat trajectory of the upper body during their jumps

• Raising the legs to achieve a “split” configuration in the air was insufficient to achieve a flat trajectory

• Raising the arms past the horizontal was necessary to achieve the linear translation illusion with both dancers

Arms High, Legs Horizontal

Initial Jump

Jump after Legs Raised to Horizontal

Jump with Legs and Arms Raised

Jump Height versus Shoulder Rise

Subject: LS PG

Actual jump height

25 cm 21 cm

Actual rise of shoulders

21 cm 19 cm

With legs raised 14 cm 13 cm

With legs and arms

0 cm 0 cm

Discussion

• The illusion of “floating” through the air or linear translating while airborne could be achieved but required that the arms elevate above horizontal

• In some dance traditions this is not a permissible motion

• The illusion could be extended further by lowering the arms and legs after the jump apex, however, this may result in a hazardous landing

References

• Lemaire, E.D. & Robertson, D.G.E. (1990) Validation of a computer simulation for planar airborne human motions. Journal of Human Movement Studies, 18:213-28.

• Laws, K. (2002) Physics and the Art of Dance. New York: Oxford Press.

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