| dc.creator |
Marrero, Juan Carlos |
|
| dc.creator |
Martín de Diego, David |
|
| dc.creator |
Martínez, Eduardo |
|
| dc.date |
2007-11-21T19:23:21Z |
|
| dc.date |
2007-11-21T19:23:21Z |
|
| dc.date |
2006-11-27 |
|
| dc.date.accessioned |
2017-01-31T00:58:54Z |
|
| dc.date.available |
2017-01-31T00:58:54Z |
|
| dc.identifier |
arXiv:math/0506299v2 |
|
| dc.identifier |
Nonlinearity, vol. 19, no. 6 (Jun. 2006), pp. 1313-1348. |
|
| dc.identifier |
0951-7715 |
|
| dc.identifier |
http://hdl.handle.net/10261/2283 |
|
| dc.identifier.uri |
http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2283 |
|
| dc.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. |
|
| dc.description |
This work has been partially supported by MICYT (Spain) Grants BMF 2003-01319, MTM
2004-7832 and BMF 2003-02532. |
|
| dc.description |
Peer reviewed |
|
| dc.language |
eng |
|
| dc.publisher |
Institute of Physics Publishing |
|
| dc.relation |
Preprint |
|
| dc.rights |
openAccess |
|
| dc.subject |
Discrete Mechanics |
|
| dc.subject |
Lie groupoids |
|
| dc.subject |
Lie algebroids |
|
| dc.subject |
Lagrangian Mechanics |
|
| dc.subject |
Hamiltonian Mechanics |
|
| dc.title |
Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids |
|
| dc.type |
Pre-print |
|