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

CÉDRIC M. CAMPOS, HERNÁN CENDRA, VIVIANA A. DÍAZ AND DAVID MARTÍN DE DIEGO

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS

REAL ACAD CIENCIAS EXACTAS FISICAS & NATURALES

Lugar: Madrid; Año: 2012 vol. 106 p. 225 - 234

1578-7303

Nonholonomic systems are described by the Lagrange-d´Alembert principle. The presenceof 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.