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. Applications of the results to Newton's laws are presented and their Galilean invariance is discussed.(c) 2022 Elsevier B.V. All rights reserved.