The Rolling Motion of a Ball on a Surface. New Integrals and Hierarchy of Dynamics

Details The Rolling Motion of a Ball on a Surface. New Integrals and Hierarchy of Dynamics The Rolling Motion of a Ball on a Surface. New Integrals and Hierarchy of Dynamics

2003-03-12

arxiv.org/abs/nlin/0303024v1

Regular and Chaotic Dynamics, V. 7, N 2, 2002

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, 7 figures

Scientific paper

The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and invariant measure exist. Using this case, we obtain a nonholonomic generalization of the Jacobi problem for the inertial motion of a point on an ellipsoid. For a ball rolling, it is also shown that on an arbitrary cylinder in the gravity field the ball's motion is bounded and, on the average, it does not move downwards. All the results of the paper considerably expand the results obtained by E. Routh in XIX century.

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