2020/02/29 by Fabio Botelho, Botelho, Fabio
Engineering · Mathematics · Physics and Astronomy · #53Z05 #Advanced Differential Geometry Research #Dynamics and Control of Mechanical Systems #FOS: Mathematics #General Mathematics (math.GM) #Numerical methods for differential equations #math.GM #msc:53Z05
paper · pdf · doi:10.48550/arxiv.2003.00325
25 pages, minor corrections implemented, new sections added
openalex publication_date 2020/02/29 · arxiv created 2020/03/27 · arxiv updated 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion manifold has a n+1 dimensional range. It is worth emphasizing in a first approximation we have neglected the self-interaction energy part. In its second part, this article develops some formalism concerning the causal structure in a general space-time manifold. Finally, the last article section presents a result concerning the existence of a generalized solution for the world sheet manifold variational formulation.