Discrete Lagrange-d’Alembert-Poincaré equations for Euler’s disk
| Autor: | Viviana Alejandra Díaz, David Martín de Diego, Cédric M. Campos, Hernán Cendra |
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| Rok vydání: | 2011 |
| Předmět: |
Algebra and Number Theory
Applied Mathematics Semi-implicit Euler method Mathematical analysis Physics::Classical Physics Backward Euler method Symmetry (physics) Euler equations Computational Mathematics symbols.namesake Simultaneous equations Euler's formula symbols Thick disk Mathematics::Mathematical Physics Euler's Disk Geometry and Topology Analysis Mathematics |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 106:225-234 |
| ISSN: | 1579-1505 1578-7303 |
| DOI: | 10.1007/s13398-011-0053-3 |
| Popis: | Nonholonomic systems are described by the Lagrange-d’Alembert principle. The presence of symmetry leads to a reduced d’Alembert principle and to the Lagrange-d’Alembert-Poincare 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-Poincare equations for an Euler’s disk and the numerical simulation of a trajectory and its energy behavior. |
| Databáze: | OpenAIRE |
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