Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics

Standard and non-standard Lagrangians that give the same

equation of motion are significantly different in their forms, as the latter

do not have terms that clearly discernable energy-like expressions. A special

family of these Lagrangians are null Lagrangians and their gauge functions.

It is shown that non-standard null Lagrangians and their gauge functions

can be used to introduce dissipative forces to dynamical systems. With

standard null Lagrangians being known for introducing non-dissipative

forces, the presented results allow for a complete picture of novel roles

played by null Lagrangians in introducing forces to dynamics.