A new perspective on symplectic integration of constrained mechanical systems via discretization maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909419600609280 |
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| author | Liñán, María Barbero de Diego, David Martín de Almagro, Rodrigo T. Sato Martín |
| author_facet | Liñán, María Barbero de Diego, David Martín de Almagro, Rodrigo T. Sato Martín |
| contents | A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the discretization rule rather than viceversa. As a result, the constraint submanifold is exactly preserved by the symplectic discrete flow and the extension of these methods to the case of non-linear configuration spaces is doable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06786 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new perspective on symplectic integration of constrained mechanical systems via discretization maps Liñán, María Barbero de Diego, David Martín de Almagro, Rodrigo T. Sato Martín Numerical Analysis Mathematical Physics A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the discretization rule rather than viceversa. As a result, the constraint submanifold is exactly preserved by the symplectic discrete flow and the extension of these methods to the case of non-linear configuration spaces is doable. |
| title | A new perspective on symplectic integration of constrained mechanical systems via discretization maps |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2306.06786 |