Abstract
New null Lagrangians and gauge functions are derived and they are called nonstandard because their forms are different than those previously found. The invariance of the action is used to make the Lagrangians and gauge functions exact. The first exact nonstandard null Lagrangian and its gauge function for the law of inertia are obtained, and their physical implications are discussed.
Highlights
Further constraints on all arbitrary functions that appear in the standard and nonstandard, general, exact null Lagrangians (ENLs) can be imposed by considering symmetries of these Lagrangians and the resulting dynamical equations
This paper presents methods to construct null Lagrangians
The presented general standard null Lagrangians are known, but the general nonstandard null Lagrangians obtained in this paper are new
Summary
The fact that the NLs and their GFs may play an important role in physics was shown recently by using them to restore Galilean invariance of the standard Lagrangian for Newton’s laws of dynamics [35,36] and to add forces to an undriven harmonic oscillator [37] Since those previously constructed NLs resemble the standard Lagrangians, they are called here standard NLs, and their corresponding GFs become standard GFs. In this paper, the standard and nonstandard NLs and their GFs are constructed and applied to the law of inertia in Galilean space and time with the Galilean group of the metric [8,25].
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