Rolling of a homogeneous ball over a dynamically asymmetric sphere
2010, Vol. 6, No. 4, pp. 869-889
Author(s): Borisov A. V., Kilin A. A., Mamaev I. S.
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.
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