Propelling a torque controlled baton to a maximum height

Recent applications of optimal control theory to the analysis of human and animal locomotion have resulted in optimal control problems that are too complex for analytic solution. Furthermore, these problems involve unusual constraints and dynamics. In order to provide a clearer understanding of the problems involved, the much simpler but related problem of causing a baton to "jump" maximally has been completely solved via elementary methods. The solution is given in feedback form. The state space divides into several regions according to the form of the optimal control. There exist regions where many controls are globally optimal, regions where a locally optimal control and a globally optimal control both exist, and regions where a unique globally optimal control exists. Finally, some relations between these results and experimental observations in both human and animal jumping are discussed.