A dynamic approximation of balanced gymnastics landings |
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Authors: | Alison Sheets |
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Institution: | (1) Department of Mechanical & Aeronautical Engineering, University of California, Davis, One Shields Avenue, 95616-5294 Davis, CA, USA |
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Abstract: | A gymnast can balance after an uneven parallel bar dismount by contacting the ground with an appropriate body position and
angular velocity. Balanceable gymnastics landings were predicted by dividing landing into two parts: a short duration impact
phase when foot-mat contact forces are high, and a subsequent longer balancing phase during which the gymnast exerts active
control at the joints to attenuate the resulting post-impact velocities and achieve a desired motionless terminal configuration.
This paper identifies controllable sets of pre-impact landing positions and velocities for a typical female collegiate gymnast
that are feasible targets for the end of flight following a single- and double-backward somersault uneven bar dismount with
forward mass centre (CM) velocity. Simple algebraic impulse-momentum models for the impact phase determine impulses necessary
to stop the feet and slow angular velocity. After impact, a dynamic analysis is needed to determine stability because non-negligible
post-impact angular and linear velocities are possible. For almost all successfully balanced landings, ground contact occurs
with the CM positioned above the feet and between the toe and heel, because the linear impact impulses that stop the feet
also contribute to an angular impulse that slows angular momentum. Only at the largest pre-impact angular velocities following
a double-somersault dismount can contact occur with the CM in front of the toe. The gymnast is in balanceable preimpact orientations
longer when rotating more slowly and with a smaller angular momentum; therefore balance may be more likely after performing
a single-somersault dismount with a large moment of inertia. |
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Keywords: | dynamic balance gymnastics landing impact model |
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