Geometry of classical particles on curved surfaces
In this paper we consider a particle moving on a curved surface. From a variational principle, we write the equation of motion and the constraining force, both in terms of the Darboux frame adapted to the trajectory, that involves geometric information of the surface. By deformation of the trajector...
| Autores: | , , , |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | México |
| Recursos: | Universidad Autónoma Metropolitana |
| Repositorio: | Redalyc-UAM |
| OAI Identifier: | oai:redalyc.org:57050469005 |
| Acesso em linha: | https://www.redalyc.org/articulo.oa?id=57050469005 |
| Access Level: | acceso abierto |
| Palavra-chave: | Física, Astronomía y Matemáticas Curves curved surfaces particle on surfaces |
| Resumo: | In this paper we consider a particle moving on a curved surface. From a variational principle, we write the equation of motion and the constraining force, both in terms of the Darboux frame adapted to the trajectory, that involves geometric information of the surface. By deformation of the trajectory on the surface, the constraining force and equation of motion of the perturbation are obtained. We show that the transversal deformation follows a generalized Raychaudhuri equation that contains extrinsic information besides the geodesic curvature. Results in the case of surface with axial symmetry can be parametrized in terms of the angular momenta. |
|---|