A Maupertuis-type principle in relativistic mechanics and applications

2022/06/17 by Alberto Boscaggin, Boscaggin, Alberto, Walter Dambrosio +3 · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #37J45 #49S05 #70H40 #Advanced Mathematical Physics Problems #Arctic and Antarctic ice dynamics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2206.08667

openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: \frac\rm d\rm dt(\fracmx√1-|x|²/c²)=∇ V(x), x∈Ω⊂ ℝⁿ, where m, c > 0 and V: Ω→ 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.

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