The Serret-Andoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations

摘要

This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-bodydynamics and presents some new results. As is well known, the problem ofunsupported and unperturbed rigid rotator can be reduced. The availability ofthis reduction is offered by the underlying symmetry, which stems fromconservation of the angular momentum and rotational kinetic energy. When aperturbation is turned on, these quantities are no longer preserved.Nonetheless, the language of reduced description remains extremely instrumentaleven in the perturbed case. We describe the canonical reduction performed bythe Serret-Andoyer (SA) method, and discuss its applications to attitudedynamics and to the theory of planetary rotation. Specifically, we consider thecase of angular-velocity-dependent torques, and discuss thevariation-of-parameters-inherent antinomy between canonicity and osculation.Finally, we address the transformation of the Andoyer variables into theaction-angle ones, using the method of Sadov.