On Some Geometric Properties of Extremalsin the Optimal Retargeting Problemfor Spherically Symmetric Rigid Bodies

摘要

We study an optimal control problem for the spatial retargeting of a rotating rigid bodywith unit tensor of inertia. We find new geometric properties of the extremals in this variationalproblem in the nondegenerate case. We give a detailed description of the extremal "collapse" effectand its relation to the planar manoeuvre. We also show that each extremal has some rank properties.The results are based on the analysis of the system of equations obtained by applying the formalismof the Pontryagin maximum principle and on the use of first integrals.