Geometry of classical particles on curved surfaces
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Sociedad Mexicana de Física A.C.
2017
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| _version_ | 1876461526859120640 |
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| author | J.A. Santiago |
| author_facet | J.A. Santiago |
| contents | Geometry of classical particles on curved surfaces J.A. Santiago G. Chacón-Acosta O. González-Gaxiola G. Torres-Vargas Física, Astronomía y Matemáticas Curves curved surfaces particle on 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 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. 2017 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57050469005 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.63 |
| format | Artículo científico |
| id | redalyc_57050469005 |
| institution | Redalyc |
| language | en |
| publishDate | 2017 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Geometry of classical particles on curved surfaces J.A. Santiago Física, Astronomía y Matemáticas Curves curved surfaces particle on surfaces Geometry of classical particles on curved surfaces J.A. Santiago G. Chacón-Acosta O. González-Gaxiola G. Torres-Vargas Física, Astronomía y Matemáticas Curves curved surfaces particle on 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 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. 2017 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57050469005 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.63 |
| title | Geometry of classical particles on curved surfaces |
| topic | Física, Astronomía y Matemáticas Curves curved surfaces particle on surfaces |
| url | https://www.redalyc.org/articulo.oa?id=57050469005 |