Discrete second order constrained Lagrangian systems: first results
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2013
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917725684629504 |
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| author | Borda, Nicolas Fernandez, Javier Grillo, Sergio |
| author_facet | Borda, Nicolas Fernandez, Javier Grillo, Sergio |
| contents | We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1312_1941 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Discrete second order constrained Lagrangian systems: first results Borda, Nicolas Fernandez, Javier Grillo, Sergio Differential Geometry Mathematical Physics Dynamical Systems 70F25, 70G75, 70H45 (Primary) 70G45 (Secondary) We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs. |
| title | Discrete second order constrained Lagrangian systems: first results |
| topic | Differential Geometry Mathematical Physics Dynamical Systems 70F25, 70G75, 70H45 (Primary) 70G45 (Secondary) |
| url | https://arxiv.org/abs/1312.1941 |