Abstract
In order to clarify the problems associated with the application of optimal control theory to the control of animal and human movement, the much simpler but related problems of causing a rod to execute a maximal vertical or horizontal jump are solved via elementary methods. The solutions, which are given in feedback form, are nearly identical even though the performance criteria are quite different. For certain initial conditions an optimal trajectory exists along which the gradient of the optimal performance with respect to the state is discontinuous. A technique to find these trajectories is given. The extension of these results to more realistic models of humans, animals, or walking machines is described.
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