About One-Dimensional Conservative Systems with Position Depending Mass

Gustavo López Velázquez, Carlos Rodrigo Martínez Prieto

Departamento de Fsica, Universidad de Guadalajara, Guadalajara, México.
Instituto Tecnológico y Estudios Superiores de Occidente, Tlaquepaque, México.

DOI: 10.4236/jmp.2014.59093                

Abstract

For a one-dimensional conservative system with position depending mass, one deduces consistently a constant of motion, a Lagrangian, and a Hamiltonian for the nonrelativistic 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 cannot 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.

Keywords

Mass Variable Systems, Conservative System, Position Depending Mass

Conflicts of Interest

The authors declare no conflicts of interest.

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