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arXiv · 2206.08667

A Maupertuis-type principle in relativistic mechanics and applications

Alberto Boscaggin·Walter Dambrosio·Eduardo Muñoz-Hernández
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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.

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Alberto Boscaggin, Walter Dambrosio, Eduardo Muñoz-Hernández. 2022-06-17. A Maupertuis-type principle in relativistic mechanics and applications. https://arxiv.org/abs/2206.08667

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