Geodesic
Rolling of a homogeneous ball over a dynamically asymmetric sphere
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 869-889

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We consider a novel mechanical system consisting of two spherical bodies rolling over each other, which is a natural extension of the famous Chaplygin problem of rolling motion of a ball on a plane. In contrast to the previously explored non-holonomic systems, this one has a higher dimension and is considerably more complicated. One remarkable property of our system is the existence of “clandestine” linear in momenta first integrals. For a more trivial integrable system, their counterparts were discovered by Chaplygin. We have also found a few cases of integrability.
Keywords: nonholonomic constraint, rolling motion, Chaplygin ball, integral, invariant measure. 
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     author = {A. V. Borisov and A. A. Kilin and I. S. Mamaev},
     title = {Rolling of a homogeneous ball over a dynamically asymmetric sphere},
     journal = {Russian journal of nonlinear dynamics},
     pages = {869--889},
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A. V. Borisov; A. A. Kilin; I. S. Mamaev. Rolling of a homogeneous ball over a dynamically asymmetric sphere. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 869-889. http://geodesic.mathdoc.fr/item/ND_2010_6_4_a9/