This article is cited in 1 paper

Algebraic reduction of systems on two- and three-dimensional spheres

A. V. Borisov, I. S. Mamaev, S. M. Ramodanov


Abstract: The paper develops further the algebraic-reduction method for $SO(4)$-symmetrie systems on the three-dimensional sphere. Canonical variables for the reduced system are constructed both on two-dimensional and three-dimensional spheres. The method is illustrated by applying it to the two-body problem on a sphere (the bodies are assumed to interact with a potential that depends only on the geodesic distance between them) and the three-vortex problem on a two-dimensional sphere.

Keywords: Poisson structure. Lie algebra, subalgebra, Andoyer variables.

UDC: 512.77, 517.912

MSC: 70Hxx, 70G65

Received: 03.12.2008