Asymptotic Hamiltonian Reduction for the Dynamics of a Particle on a Surfaceстатья
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Статья опубликована в журнале из перечня ВАК
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Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
Аннотация:We consider the motion of a particle on the surface generated by a small perturbation of the standard
sphere. The key observation is that a trajectory of the particle has the shape of a coil, and one may qualitatively
describe the turns of the latter as a precessing great circle of the sphere. Thus, we change the configuration space
of the initial problem for the space of great circles on the sphere. The construction enables us to derive a subsidiary
Hamiltonian system having the shape of equations for the top with a 4th order Hamiltonian. The subsidiary
system provides a detailed asymptotic description of the particle’s motion in terms of graphs on the standard
sphere.