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

2008, Vol. 4, No. 4, pp.  407-416

Author(s): Borisov A. V., Mamaev I. S., Ramodanov S. M.

The paper develops further the algebraic-reduction method for $SO(4)$-symmetric 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
Citation: Borisov A. V., Mamaev I. S., Ramodanov S. M., Algebraic reduction of systems on two- and three-dimensional spheres, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 4, pp.  407-416
DOI:10.20537/nd0804002