Best pole vaulting using non-causal dynamics

There is no field and track event like pole vaulting which sets free the pole's properties to enable a vaulter to yield great jumping performance. The best choice of a pole should convert the total vaulter's take-off kinetic energy to the potential energy. However, this needs perfect matching with the dynamics. Studying non-causal dynamics of a vaulting model enables one to start from the desired objective to finally match feasible take-off velocities associated with the optimal stiffness of the pole. To this end, a boundary value problem is well defined and a shooting method is proposed. Examples are given to verify the proposed method.