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Poisson structure of the reversible 1:1 resonance

✍ Scribed by Thomas J. Bridges

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
473 KB
Volume
112
Category
Article
ISSN
0167-2789

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✦ Synopsis

Vector fields that are reversible -but non-Hamiltonian -are considered in the neighborhood of a 1 : 1 resonance. It is found that the normalized vector field has a hidden Poisson structure on the orbit space that is reminiscent of the equations governing the rigid body in mechanics. The theory is used to give a geometric characterization of the phase space in the neighborhood of a reversible 1 : 1 resonance. Certain similarities, and also essential differences, with the Hamiltonian 1 : 1 resonance are found.

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