New superintegrable system on a sphere

    2009, Vol. 5, No. 4, pp.  455-462

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

    We consider the motion of a material point on the surface of a sphere in the field of 2n+1 identical Hooke centers (singularities with elastic potential) lying on a great circle. Our main result is that this system is superintegrable. The property of superintegrability for this system has been conjectured by us in [3], where the structure of a superintegral of arbitrarily high odd degree in momemnta was outlined. We also indicate an isomorphism between this system and the one-dimensional N-particle system discussed in the recent paper [13] and show that for the latter system an analogous superintegral can be constructed.
    Keywords: superintegrable systems, systems with a potential, Hooke center
    Citation: Borisov A. V., Kilin A. A., Mamaev I. S., New superintegrable system on a sphere, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 4, pp.  455-462

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