Year: 2010
Type: preprint
Abstract: We consider geodesics on the surfaces obtained by weak deformations of the standard 2D-sphere. The dynamics of a particle on the surface can be asymptotically described by the averaged evolution of the particle's angular momentum. It is shown that the system describing this evolution has a Hamiltonian, which is obtained by applying the Funk transform to the function defining the deviation of the surface from the standard sphere. This system has the 2D-sphere as its phase space, so it is integrable and its trajectories admit of topological description in terms of its phase portrait on the sphere.
Source: arXiv (Cornell University)
Author: Sinitsyn, D. O.
Institution: Lomonosov Moscow State University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1797106287