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Asymptotic Hamiltonian reduction for the dynamics of a particle on a surface

V. L. Golo·D. O. Sinitsyn
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Abstract

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a subsidiary Hamiltonian system that has the form of equations for the top with a 4-th order Hamiltonian, and provides the detailed asymptotic description of the particle's motion in terms of graphs on the standard sphere.

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V. L. Golo, D. O. Sinitsyn. 2005-12-10. Asymptotic Hamiltonian reduction for the dynamics of a particle on a surface. https://arxiv.org/abs/math-ph/0512032

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