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Hannay-Berry phase and the restricted three-vortex problem

✍ Scribed by Paul K. Newton

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
523 KB
Volume
79
Category
Article
ISSN
0167-2789

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✦ Synopsis

Asymptotic expansions for the Hannay-Berry phase are computed for a class of Hamiltonian systems in perturbed actionangle form with slowly varying parameters, where the parameters recur on a slow time scale. A multi-scale perturbation method is used which in principle can be carried to any desired order of accuracy. As a specific application, we use the method to examine the restricted three-vortex problem, a completely integrable configuration of two co-rotating point vortices a distance D apart, and a tracer particle rotating around one of the vortices with distance r. In the asymptotic limit r/D ~ e, we compute the particle trajectory through O(e) and find that the Hannay-Berry phase is given by A0 ~ ~-+ ~rRo/D + O( lID 2) where R0 is the conserved action.

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