Abstract
The setting for this study is time-optimal reorientation maneuvers for a rigid-body. Analysis of the dynamic model reveals certain symmetries among solutions for a class of rest-to-rest maneuvers. An operator-theo retic approach is used to formalize the analysis and the set of operators is shown to form a commutative group. For extremal trajectories, a second group of transformatio ns is identified: these are mappings between the adjoint variables. The two groups are shown to be homomorphic. A particular subgroup of the adjoints maps is highlighted and used to generate several distinct extremal trajectories from a single known one. A number of extremal trajectories, shown graphically, supplement and illustrate the analytical considerations.
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