The Lagrange-D’Alembert-Poincaré equations and integrability for the Euler’s disk |
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Authors: | H Cendra V A Díaz |
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Institution: | (1) Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahia Blanca, Argentina;(2) CONICET, Argentina |
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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. |
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Keywords: | 70F25 37J60 70H33 |
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