The Jacobi integral in nonholonomic mechanics

A. V. Borisov ; I. S. Mamaev ; I. A. Bizyaev

Russian journal of nonlinear dynamics, Tome 11 (2015) no. 2, pp. 377-396.

Résumé

In this paper we discuss conditions for the existence of the Jacobi integral (that generalizes energy) in systems with inhomogeneous and nonholonomic constraints. As an example, we consider in detail the problem of motion of the Chaplygin sleigh on a rotating plane and the motion of a dynamically symmetric ball on a uniformly rotating surface. In addition, we discuss illustrative mechanical models based on the motion of a homogeneous ball on a rotating table and on the Beltrami surface.

Détail

Keywords: nonholonomic constraint, Jacobi integral, Chaplygin sleigh, rotating table, Suslov problem.

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