The Lagrange-D Alembert-Poincare Equations and Intehrability for the Eulers Disk

CENDRA, H.; DIAZ, V.A.

REGULAR AND CHAOTIC DYNAMICS

Turpion, Russian Acad. of Sciences

Lugar: Moscu; Año: 2007 vol. 12 p. 56 - 67

1560-3547

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 reducedD’Alembert’s principle and to the Lagrange–D’Alembert–Poincare´ reduced equations. The case ofrolling 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 showhow the reduced system can be transformed into a single second order equation, which is anhypergeometric equation. 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 reducedD’Alembert’s principle and to the Lagrange–D’Alembert–Poincare´ reduced equations. The case ofrolling 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 showhow the reduced system can be transformed into a single second order equation, which is anhypergeometric equation.