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.
Keywords:
nonholonomic systems, symmetry, integrability, Euler's disk
Citation:
Cendra H., Diaz V. A., The Lagrange–D'Alembert–Poincaré Equations and Integrability for the Euler's Disk, Regular and Chaotic Dynamics,
2007, Volume 12, Number 1,
pp. 56-67