This article is cited in 34 papers

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

P. Gurfil^a, A. Elipe^b, W. Tangren^c, M. Efroimsky<sup>c

a</sup> Faculty of Aerospace Engineering, Technion–Israel Institute of Technology, Haifa, 32000 Israel
^b Grupo de Mecanica Espacial, Universidad de Zaragoza, Zaragoza, 50009 Spain
^c US Naval Observatory, Washington DC, 20392 USA

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, 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 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 action-angle ones, using the method of Sadov.

Keywords: nonlinear stabilization, Hamiltonian control systems, Lyapunov control.

MSC: 70E20, 53D22, 70F15

Received: 24.07.2006
Accepted: 08.07.2007

Language: English

DOI: 10.1134/S156035470704003X

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