I. S. MAMAEV Institute of computer science 426034, Russia, Izhevsk Universitetskaya St., 1 E-mail: mamaev@rcd.ru NEW CASES WHEN THE INVARIANT MEASURE AND FIRST INTEGRALS EXIST IN THE PROBLEM OF A BODY ROLLING ON A SURFACE Received September 16, 2003 DOI: 10.1070/RD2003v008n03ABEH000249 Some new cases when the invariant measure and an additional first integral exist in the problem of a rigid body rolling on a sphere and on an ellipsoid are discussed in the paper. ... Rolling of a ball on a surface. ...

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