Please use this identifier to cite or link to this item:
http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2283| Title: | Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids |
| Keywords: | Discrete Mechanics Lie groupoids Lie algebroids Lagrangian Mechanics Hamiltonian Mechanics |
| Publisher: | Institute of Physics Publishing |
| Description: | The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Legendre transformations we define the Hamiltonian evolution operator which is a symplectic map with respect to the canonical symplectic 2-section on the prolongation of the dual of the Lie algebroid of the given groupoid. The equations we get include as particular cases the classical discrete Euler-Lagrange equations, the discrete Euler-Poincaré and discrete Lagrange-Poincaré equations. Our results can be important for the construction of geometric integrators for continuous Lagrangian systems. This work has been partially supported by MICYT (Spain) Grants BMF 2003-01319, MTM 2004-7832 and BMF 2003-02532. Peer reviewed |
| URI: | http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2283 |
| Other Identifiers: | arXiv:math/0506299v2 Nonlinearity, vol. 19, no. 6 (Jun. 2006), pp. 1313-1348. 0951-7715 http://hdl.handle.net/10261/2283 |
| Appears in Collections: | Digital Csic |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.