Regular and Chaotic Dynamics

, Volume 12, Issue 1, pp 56–67 | Cite as

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

  • H. Cendra
  • V. A. Díaz
Research Articles

Abstract

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.

MSC2000 numbers

70F25 37J60 70H33 

Key words

nonholonomic systems symmetry integrability Euler’s disk 

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • H. Cendra
    • 1
    • 2
  • V. A. Díaz
    • 1
    • 2
  1. 1.Departamento de MatemáticaUniversidad Nacional del SurBahia BlancaArgentina
  2. 2.CONICETArgentina

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