Lagrangians and Hamiltonians for one-dimensional systems

Abstract

An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system that has certain quasi-relativistic properties. A new method based on a Taylor series expansion is used to obtain the associated Hamiltonian for this system. These results have the usual expression for a conservative system when the dissipation parameter goes to zero. An example of this approach is given.

To be published in the International Journal of Theoretical Physics

Cited by in corpus (2)

• A direct approach to the construction of standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients
• Relativistic motion with linear dissipation