Geodesic
New superintegrable system on a sphere
Russian journal of nonlinear dynamics, Tome 5 (2009) no. 4, pp. 455-462.

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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. 
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     author = {A. V. Borisov and A. A. Kilin and I. S. Mamaev},
     title = {New superintegrable system on a sphere},
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A. V. Borisov; A. A. Kilin; I. S. Mamaev. New superintegrable system on a sphere. Russian journal of nonlinear dynamics, Tome 5 (2009) no. 4, pp. 455-462. http://geodesic.mathdoc.fr/item/ND_2009_5_4_a0/