Optimal rigid body motions,part 1: Approximate formulation

Optimal rigid body angular motions are investigated in the absence of direct control over one of the angular velocity components, via an approximate dynamic model. An analysis of first-order necessary conditions for optimality with the proposed model reveals that, over a large range of boundary conditions, there are, in general, several distinct extremal solutions. A classification in terms of subfamilies of extremal solutions is presented. Second-order necessary conditions are investigated to establish local optimality for the candidate minimizers.This work was supported in part by DARPA Contract No. ACMP-F49620-87-C-0116 and by Air Force Grant AFOSR-89-0001.