2014/04/09 by Gustavo V. López, Gustavo V. Lopez, Lopez, Gustavo V. +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical Physics (physics.class-ph) #FOS: Physical sciences #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1404.2650
7 pages, two figures
arxiv created 2014/04/09 · openalex publication_date 2014/04/09 · arxiv updated 2014/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a one-dimensional conservative systems with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the non relativistic case. With these functions, one shows the trajectories on the spaces (x,v) and (x,p) for a linear position depending mass. For the relativistic case, the Lagrangian and Hamiltonian can not be given explicitly in general. However, we study the particular system with constant force and mass linear dependence on the position where the Lagrangian can be found explicitly, but the Hamiltonian remains implicit in the constant of motion.