A Maupertuis-type principle in relativistic mechanics and applications

DOI10.1007/S00526-023-02430-9arXiv2206.08667MaRDI QIDQ6402358

Alberto Boscaggin, Walter Dambrosio, Eduardo Muñoz-Hernández

Publication date: 17 June 2022

Abstract: We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: ${\displaystyle }$ frac{ m d}{{ m d}t}left(frac{mdot{x}}{sqrt{1-|dot{x}|^2/c^2}} ight)= abla V(x),qquad xinOmega subset mathbb{R}^n, ${\displaystyle }$ where $m,c>0$ and $V:OmegaomathbbR$ 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.

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Dynamical systems in classical and celestial mechanics (37N05) Variational principles of physics (49S05) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

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