The Motion of a Gyrostat in a Central Gravitational Field: Phase Portraits of an Integrable Case

DOI

10.2991/jnmp.2008.15.s3.6How to use a DOI?

Abstract

In this paper we describe the Hamiltonian dynamics, in some invariant manifolds of the mo- tion of a gyrostat in Newtonian interaction with a spherical rigid body. Considering a first integrable approximation of this roto-translatory problem, by means of Liouville-Arnold the- orem and some specifics techniques, we obtained a complete topological classification of the phase flow associated to this system. The action-angle variables regions are obtained. These variables allow us to calculate the modified Keplerian elements of this problem useful to elab- orate a perturbation theory. The results of this work have a direct application to the study of two body roto-translatory pro-blems where the rotation of one of them influences strongly in the orbital motion of the system. In particular, we can apply these results to binary asteroids.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M.C. Balsas
AU  - E.S. Jiménez
AU  - J.A. Vera
PY  - 2008
DA  - 2008/10/01
TI  - The Motion of a Gyrostat in a Central Gravitational Field: Phase Portraits of an Integrable Case
JO  - Journal of Nonlinear Mathematical Physics
SP  - 53
EP  - 64
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.6
DO  - 10.2991/jnmp.2008.15.s3.6
ID  - Balsas2008
ER  -