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

Abstract

This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics 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 offered by the underlying symmetry, which 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 Serret-Andoyer (SA) method, and discuss its applications to attitude dynamics and to the theory of planetary rotation. Specifically, 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 the action-angle ones, using the method of Sadov.

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• Direct measurement of diurnal polar motion by ring laser gyroscopes
• Gauge Freedom in Orbital Mechanics
• The empirical Earth rotation model from VLBI observations

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