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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.

Information

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 

References

Cid, R. and Correas, J.M., 1973: Actas I Jornadas Matemáticas Hispano-Lusas, 439–452.Google Scholar
Cid, R. and Vigueras, A., 1990: Rev. Acad. Ciencias. Zaragoza (Spain), 45, 83–93.Google Scholar
Deprit, A., 1967: Free rotation of a rigid body studied in the phase plane. Amer. J. Phys. 35, 424–428.Google Scholar
Deprit, A. and Elipe, A., 1993: Complete reduction of the Euler-Poinsot problem. J. of the Astronautical Sciences, 41, 4, 603–628.Google Scholar
Kinoshita, H., 1972: First-order perturbations of the two finite body problem. Publ. Astron. Soc. Japan, 24, 423–457.Google Scholar
Kinoshita, H., 1977: Theory of the rotation of the rigid earth. Celestial Mechanics, 15, 277–326.Google Scholar
Kinoshita, H., 1992: Analytical expansions of torque-free motions for short and long axis modes. Celestial Mechanics and Dynamical Astronomy, 53, 365–375.Google Scholar
Sadov, A., 1970: The action-angle variables in the Euler-Poinsot problem. PMM, 34, 962–964.Google Scholar
Vigueras, A., 1983: Movimiento rotatorio de giróstatos y aplicaciones. Ph. Dissertation. Univ. de Zaragoza, Spain.Google Scholar