A Maupertuis-type principle in relativistic mechanics and applications
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2023
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Springer
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Boscaggin, A., Dambrosio, W. & Muñoz-Hernández, E. A Maupertuis-type principle in relativistic mechanics and applications. Calc. Var. 62, 95 (2023). https://doi.org/10.1007/s00526-023-02430-9
Abstract
We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: d/dt (mx˙/√1 −|˙x|2/c2) = ∇V(x), x ∈ ⊂ Rn, where m, c > 0 and V : → R is a function of class C1. As an application, we prove the existence of multiple periodic solutions with prescribed energy for a relativistic N-centre type problem in the plane.