A dynamic approximation of balanced gymnastics landings

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.