The Lagrange-D’Alembert-Poincaré equations and integrability for the Euler’s disk

Regular and Chaotic Dynamics - Tập 12 - Trang 56-67 - 2007
H. Cendra1,2, V. A. Díaz1,2
1Departamento de Matemática, Universidad Nacional del Sur, Bahia Blanca, Argentina
2CONICET, Argentina

Tóm tắt

Nonholonomic systems are described by the Lagrange-D’Alembert’s principle. The presence of symmetry leads, upon the choice of an arbitrary principal connection, to a reduced D’Alembert’s principle and to the Lagrange-D’Alembert-Poincaré reduced equations. The case of rolling constraints has a long history and it has been the purpose of many works in recent times. In this paper we find reduced equations for the case of a thick disk rolling on a rough surface, sometimes called Euler’s disk, using a 3-dimensional abelian group of symmetry. We also show how the reduced system can be transformed into a single second order equation, which is an hypergeometric equation.

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Regular and Chaotic Dynamics

Tập 12

56-67

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