Discrete Lagrange-d’Alembert-Poincaré equations for Euler’s disk

  • Cédric M. Campos
  • Hernán Cendra
  • Viviana Alejandra DíazEmail author
  • David Martín de Diego
Original Paper


Nonholonomic systems are described by the Lagrange-d’Alembert principle. The presence of symmetry leads to a reduced d’Alembert principle and to the Lagrange-d’Alembert-Poincaré equations. First, we briefly recall from previous works how to obtain these reduced equations for the case of a thick disk rolling on a rough surface using a three-dimensional abelian group of symmetries. The main results of the present paper are the calculation of the discrete Lagrange-d’Alembert-Poincaré equations for an Euler’s disk and the numerical simulation of a trajectory and its energy behavior.


Euler’s disk Discrete Lagrange-d’Alembert-Poincaré equations 

Mathematics Subject Classification (2000)

53Z 70F25 70H 37J 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Cédric M. Campos
    • 1
  • Hernán Cendra
    • 2
    • 3
  • Viviana Alejandra Díaz
    • 2
    Email author
  • David Martín de Diego
    • 1
  1. 1.Instituto de Ciencias Matemáticas, Campus de Cantoblanco, UAMMadridSpain
  2. 2.Departamento de MatemáticaUniversidad Nacional del SurBahía BlancaArgentina
  3. 3.CONICETBuenos AiresArgentina

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