One Dimensional Relativistic Free Particle in a Quadratic Dissipative Medium

Abstract

The deduction of a constant of motion, a Lagrangian, and a Hamiltonian for relativistic particle moving in a dissipative medium characterized by a force which depends on the square of the velocity of the particle is done. It is shown that while the trajectories in the space ( x , v ), defined by the constant of motion, look as one might expected, the trajectories in the space ( x , p ), defined by the Hamiltonian, have an odd behavior.<