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The closedness of orbits of central forces is addressed in a threedimensional space in which the Poisson bracket among the coordinates is that ofthe SU(2) Lie algebra. In particular it is shown that among problems withspherically symmetric potential energies, it is only the Kepler problem forwhich all of the bounded orbits are closed. In analogy with the case of theordinary space, a conserved vector (apart from the angular momentum) isexplicitly constructed, which is responsible for the orbits being closed. Thisis the analog of the Laplace-Runge-Lenz vector. The algebra of the constants ofthe motion is also worked out.

Closedness of orbits in a space with SU(2) Poisson structure