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The Hamiltonian Dynamics of The Two Gyrostats Problem

Published online by Cambridge University Press:  12 April 2016

F. Mondejar  and
A. Vigueras
F. Mondejar
Affiliation:
Departamento de Matemática Aplicada, E. T. S.I.I., Universidad de Murcia, Paseo Alfonso XIII, 30203 Cartagena (Murcia), SpainE-mail:fmalacid@plc.um.esandvigueras@plc.um.es
A. Vigueras
Affiliation:
Departamento de Matemática Aplicada, E. T. S.I.I., Universidad de Murcia, Paseo Alfonso XIII, 30203 Cartagena (Murcia), SpainE-mail:fmalacid@plc.um.esandvigueras@plc.um.es

Abstract

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The problem of two gyrostats in a central force field is considered. We prove that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system posseses symmetries. Using them we perform the reduction of the number of degrees of freedom. We show that at every stage of the reduction process, equations of motion are Hamiltonian and give explicit forms corresponding to non-canonical Poissson brackets. Finally, we study the case where one of the gyrostats has null gyrostatic momentum and we study the zero and the second order approximation, showing that all equilibria are unstable in the zero order approximation.

Type
Analytical and Numerical Tools
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 303 - 312
Copyright
Copyright © Kluwer 1999

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