Geodesic
Algebraic reduction of systems on two- and three-dimensional spheres
Russian journal of nonlinear dynamics, Tome 4 (2008) no. 4, pp. 407-416.

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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.
Mots-clés : Poisson structure. Lie algebra, subalgebra, Andoyer variables. 
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     title = {Algebraic reduction of systems on two- and three-dimensional spheres},
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A. V. Borisov; I. S. Mamaev; S. M. Ramodanov. Algebraic reduction of systems on two- and three-dimensional spheres. Russian journal of nonlinear dynamics, Tome 4 (2008) no. 4, pp. 407-416. http://geodesic.mathdoc.fr/item/ND_2008_4_4_a1/