0
2013
Impact Factor

Viviana Diaz

Avda. Alem 1253 - 2 Piso, 8000, Bahia Blanca, Argentina
Departamento de Matematica, Universidad Nacional del Sur, Bahia Blanca

Publications:

Cendra H., Diaz V. A.
The Lagrange–D'Alembert–Poincaré Equations and Integrability for the Euler's Disk
2007, vol. 12, no. 1, pp.  56-67
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.
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, vol. 12, no. 1, pp. 56-67
DOI:10.1134/S1560354707010054
Cendra H., Diaz V. A.
The Lagrange–D'Alembert–Poincaré equations and integrability for the rolling disk
2006, vol. 11, no. 1, pp.  67-81
Abstract
Classical nonholonomic systems are described by the Lagrange–d'Alembert principle. The presence of symmetry leads, upon the choice of an arbitrary principal connection, to a reduced variational principle and to the Lagrange–d'Alembert–Poincaré reduced equations. The case of rolling bodies has a long history and it has been the purpose of many works in recent times, in part because of its applications to robotics. In this paper we study the classical example of the rolling disk. We consider a natural abelian group of symmetry and a natural connection for this example and obtain the corresponding Lagrange–d'Alembert–Poincaré equations written in terms of natural reduced variables. One interesting feature of this reduced equations is that they can be easily transformed into a single ordinary equation of second order, which is a Heun's equation.
Keywords: rolling disk, nonholonomic mechanics, integrability, Heun's equation
Citation: Cendra H., Diaz V. A.,  The Lagrange–D'Alembert–Poincaré equations and integrability for the rolling disk , Regular and Chaotic Dynamics, 2006, vol. 11, no. 1, pp. 67-81
DOI:10.1070/RD2006v011n01ABEH000335

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