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Analytical integration of a generalized Euler-Poinsot problem: Applications

Published online by Cambridge University Press:  25 May 2016

R. Molina  and
A. Vigueras
R. Molina
Affiliation:
Dpto de Matematica Aplicada y Estadistica Esc. Politecnica Superior de Cartagena, U. Murcia, Spain
A. Vigueras
Affiliation:
Dpto de Matematica Aplicada y Estadistica Esc. Politecnica Superior de Cartagena, U. Murcia, Spain

Abstract

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We consider a generalized Euler-Poinsot problem for a stationary gyrostat whose first two components of the gyrostatic momentum are null. The problem is formulated in the Serret-Andoyer canonical variables and analytically integrated by means of the Hamilton-Jacobi equation in terms of elliptic functions and integrals. The obtained solutions are just the same as those for rigid bodies if a specific constant is annulled. Finally, two applications are proposed: 1) to obtain the action-angle variables of this problem, and 2) to the problem of the rotation of the Earth, using a triaxial gyrostat as a model.

Type
Part VI - Earth and Deformable Celestial Bodies
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 249 - 250
Copyright
Copyright © Kluwer 1996 

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