A Maupertuis-type principle in relativistic mechanics and applications
Abstract
We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: $$ \frac{\rm d}{{\rm d}t}\left(\frac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right)=\nabla V(x),\qquad x\in\Omega \subset \mathbb{R}^n, $$ where $m, c > 0$ and $V: \Omega \to \mathbb{R}$ is a function of class $C^1$. As an application, we prove the existence of multiple periodic solutions with prescribed energy for a relativistic $N$-centre type problem in the plane.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.08667
- arXiv:
- arXiv:2206.08667
- Bibcode:
- 2022arXiv220608667B
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematical Physics;
- 37J45;
- 49S05;
- 70H40
- E-Print:
- 33 pages