The action principle for dissipative systems

TL;DR

This paper redefines and generalizes the action principle for dissipative systems using mixed integer and fractional derivatives, fixing previous inconsistencies and applying it to friction and charged particle problems.

Contribution

It introduces a mathematically consistent quadratic Lagrangian framework for non-conservative systems involving fractional derivatives.

Findings

Successfully formulates a quadratic Lagrangian for a particle with friction.

Applies the generalized action principle to the classical charged particle problem.

Fixes mathematical inconsistencies in previous dissipative action principles.

Abstract

In the present work we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to formulate a quadratic Lagrangian for non-conservative systems, the Lagrangian functions proposed depend on mixed integer order and fractional order derivatives. As examples, we formulate a quadratic Lagrangian for a particle under a frictional force proportional to the velocity, and to the classical problem of an accelerated point charge.