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Standard and non-standard Lagrangians that give the same equation of motionare significantly different in their forms, as the latter do not have termsthat clearly discernable energy-like expressions. A special family of theseLagrangians are null Lagrangians and their gauge functions. It is shown thatnon-standard null Lagrangians and their gauge functions can be used tointroduce dissipative forces to dynamical systems. With standard nullLagrangians being known for introducing non-dissipative forces, the presentedresults allow for a complete picture of novel roles played by null Lagrangiansin introducing forces to dynamics. Applications of the results to Newton's lawsare presented and their Galilean invariance is discussed.

Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics