Comment on "Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficientes"

TL;DR

This paper discusses methods to generate new non-standard Lagrangians for dissipative dynamical systems, expanding the class of equations that can be described by a Lagrangian framework.

Contribution

It introduces a procedure to derive new non-standard Lagrangians from existing ones, linking them to new equations of motion.

Findings

New non-standard Lagrangians can be systematically generated.

Each non-standard Lagrangian corresponds to a unique equation of motion.

The approach broadens the applicability of Lagrangian methods to dissipative systems.

Abstract

Z.E. Musielak has reported in 2008 J. Phys. A: Math. Theor. {\bf 41} 055205 methods to obtain standard and non-standard Lagrangians and identify classes of equations of motion that admit a Lagrangian description. In this comment we show how to obtain new non-standard Lagrangians using the non-standard Lagrangians previously found. In particular, it is demonstrated that for every non-standard Lagrangian one can generate a new non-standard Lagrangian associated to a new equation of motion.