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.

Source link


Leave A Reply