REVIEW ARTICLES The SerretAndoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations

AbstractThis paper reviews the SerretAndoyer (SA) canonical formalism in rigid-body dynam-ics, and presents some new results. As is well known, the problem of unsupported and unperturbed rigid rotator can be reduced. The availability of this reduction is oered by the underlying symmetry, that stems from conservation of the angular momentum and rotational kinetic energy. When a perturbation is turned on, these quantities are no longer preserved. Nonetheless, the language of reduced description remains extremely instrumental even in the perturbed case. We describe the canonical reduction performed by the SerretAndoyer (SA) method, and discuss its applications to attitude dynamics and to the theory of planetary rotation. Specically, we consider the case of angular-velocity-dependent torques, and discuss the variation-of-parameters-inherent antinomy between canonicity and osculation. Finally, we address the transformation of the Andoyer variables into action-angle ones, using the method of Sadov