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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
The Lagrange–D'Alembert–Poincaré Equations and Integrability for the Euler's Disk
H. Cendra, V. Diaz Departamento de Matematica, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahia Blanca and CONICET, Argentina
Аннотация:
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.
Ключевые слова:
nonholonomic systems, symmetry, integrability, Euler's disk.
Поступила в редакцию: 12.09.2005 Принята в печать: 25.09.2006
Образец цитирования:
H. Cendra, V. Diaz, “The Lagrange–D'Alembert–Poincaré Equations and Integrability for the Euler's Disk”, Regul. Chaotic Dyn., 12:1 (2007), 56–67
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd611 https://www.mathnet.ru/rus/rcd/v12/i1/p56
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