The Serret-Andoyer Formalism in Rigid-Body Dynamics: 1. 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, 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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA471055

Entities

People

  • A. Elipe
  • M. Efroimsky
  • P. Gurfil
  • W. Tangren

Organizations

  • United States Naval Observatory

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Angular Momentum
  • Celestial Mechanics
  • Computational Fluid Dynamics
  • Coordinate Systems
  • Differential Equations
  • Dynamics
  • Equations
  • Equations Of Motion
  • Euler Angles
  • Kinetic Energy
  • Mechanics
  • Orbital Elements
  • Orbits
  • Perturbations
  • Symmetry
  • Time Dependence
  • Trajectories

Readers

  • Marine Propulsion Engineering and Naval Architecture
  • Plasma Physics / Magnetohydrodynamics
  • Structural Dynamics.