The Lagrange-D’Alembert-Poincaré equations and integrability for the Euler’s disk
| Autor: | Viviana Alejandra Díaz, Hernán Cendra |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Nonholonomic system
Matemáticas SYMMETRY Mathematical analysis EULER'S DISK INTEGRABILITY NONHOLONOMIC SYSTEMS Physics::Classical Physics Symmetry (physics) Matemática Pura Connection (mathematics) symbols.namesake Mathematics (miscellaneous) Poincaré conjecture symbols Thick disk Euler's formula Euler's Disk Abelian group CIENCIAS NATURALES Y EXACTAS Mathematics |
| Zdroj: | Regular and Chaotic Dynamics. 12:56-67 |
| ISSN: | 1468-4845 1560-3547 |
| DOI: | 10.1134/s1560354707010054 |
| Popis: | 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. Fil: Cendra, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina Fil: Diaz, Viviana Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina |
| Databáze: | OpenAIRE |
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