Merry-go-round and time-dependent symplectic forms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908748455346176 |
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| author | Frauenfelder, Urs Weber, Joa |
| author_facet | Frauenfelder, Urs Weber, Joa |
| contents | In the merry-go-round fictitious forces are acting like centrifugal force and Coriolis force. Like the Lorentz force Coriolis force is velocity dependent and, following Arnold, can be modeled by twisting the symplectic form. If the merry-go-round is accelerated an additional fictitious force shows up, the Euler force.
In this article we explain how one deals symplectically with the Euler force by considering time-dependent symplectic forms. It will turn out that to treat the Euler force one also needs time-dependent primitives of the time-dependent symplectic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Merry-go-round and time-dependent symplectic forms Frauenfelder, Urs Weber, Joa Symplectic Geometry Mathematical Physics Dynamical Systems Classical Physics 53D-XX 70H-XX 37C-XX In the merry-go-round fictitious forces are acting like centrifugal force and Coriolis force. Like the Lorentz force Coriolis force is velocity dependent and, following Arnold, can be modeled by twisting the symplectic form. If the merry-go-round is accelerated an additional fictitious force shows up, the Euler force. In this article we explain how one deals symplectically with the Euler force by considering time-dependent symplectic forms. It will turn out that to treat the Euler force one also needs time-dependent primitives of the time-dependent symplectic forms. |
| title | Merry-go-round and time-dependent symplectic forms |
| topic | Symplectic Geometry Mathematical Physics Dynamical Systems Classical Physics 53D-XX 70H-XX 37C-XX |
| url | https://arxiv.org/abs/2601.02338 |