Variational reduction of homogenous Lagrangian systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909020141387776 |
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| author | Fernández, Javier Grillo, Sergio Marrero, Juan Carlos Padrón, Edith |
| author_facet | Fernández, Javier Grillo, Sergio Marrero, Juan Carlos Padrón, Edith |
| contents | In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of the system can be reconstructed up to quadratures from the critical points of the reduced variational principle. Also, we characterize the mentioned critical points in terms of a set of ordinary differential equations which are the scaling analogue of the Lagrange-Poincaré equations. Finally, we study if the homogeneous Lagrangian systems are naturally related or not with the Herglotz variational principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variational reduction of homogenous Lagrangian systems Fernández, Javier Grillo, Sergio Marrero, Juan Carlos Padrón, Edith Differential Geometry Mathematical Physics Primary 70H03, 70H30, 70G65, Secundary 53D05, 53D10 In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of the system can be reconstructed up to quadratures from the critical points of the reduced variational principle. Also, we characterize the mentioned critical points in terms of a set of ordinary differential equations which are the scaling analogue of the Lagrange-Poincaré equations. Finally, we study if the homogeneous Lagrangian systems are naturally related or not with the Herglotz variational principle. |
| title | Variational reduction of homogenous Lagrangian systems |
| topic | Differential Geometry Mathematical Physics Primary 70H03, 70H30, 70G65, Secundary 53D05, 53D10 |
| url | https://arxiv.org/abs/2605.05517 |