Hamiltonian for a Relativistic Particle with Linear Dissipation

Abstract

A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The hamiltonian for a relativistic particle with linear dissipation is obtained. An example of this approach is given.

Fractional Dynamics of Relativistic Particle

“…Note that a one-dimensional relativistic particle with dissipation is considered in Refs. [13,14]. The Lagrangian and Hamiltonian functions for one-dimensional relativistic particles with linear dissipation are suggested.…”

“…The fractional equations of motion describes power-law memory effects that correspond to intrinsic dissipative processes in the relativistic systems. Note that relativistic particle with dissipation is discussed in [13,14]. In Refs.…”

“…In Refs. [13,14], the Lagrangian and Hamiltonian functions for one-dimensional relativistic particles with linear dissipation are suggested. In general, non-Hamiltonian and dissipative n-dimensional systems with n > 1 cannot be described by Hamiltonian or Lagrangian since the Helmholtz's conditions for these systems are not satisfied [15].…”

The Interaction of a Circularly Orbiting Electromagnetic Harmonic Wave with an Electron Having a Constant Time Independent Drift Velocity

“…The Einstein relativistic energy relation [7] is already used as a Hamiltonian to derive the Klein-Gordon equation [4]. More recently relativistic Hamiltonians are discussed in the references [8][9][10][11][12].…”