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.
    Keywords: nonholonomic constraint, rolling motion, Chaplygin ball, integral, invariant measure
    Citation: Borisov A. V., Kilin A. A., Mamaev I. S., Rolling of a homogeneous ball over a dynamically asymmetric sphere, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 4, pp.  869-889

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