Free motion on the Poisson plane and sphere

Details Free motion on the Poisson plane and sphere Free motion on the Poisson plane and sphere

1996-12-04

arxiv.org/abs/dg-ga/9612006v1

Mathematics

Differential Geometry

LaTeX, 9 pages

Scientific paper

Poisson plane and sphere --- homogeneous spaces of Poisson groups E(2) and SU(2) (resp.) --- have phase spaces (corresponding symplectic groupoids), in which a free Hamiltonian is naturally defined. We solve the equations of motion and point out some unexpected features: free motion on the plane is bounded (periodic) and free trajectories on the sphere are all circles except the big ones.

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