The Hamiltonian Dynamics of the Two Gyrostats Problem |
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Authors: | F Mondejar A Vigueras |
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Institution: | (1) Departamento de Matemática Aplicada, E. T. S.I.I., Universidad de Murcia, Paseo Alfonso XIII, 30203 Cartagena (Murcia), Spain |
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Abstract: | 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 Poisson 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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | |
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