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