Sufficiency conditions under which a lagrangian is an ordinary divergence

Abstract

An expression is derived for the variation of Lagrangians which are such that the set of admissible variables of variation is star-shaped. If such a Lagrangian leads to identically vanishing Euler-Lagrange expressions then it is shown that under suitable circumstances the Lagrangian in question must be an ordinary divergence. Furthermore, an expression is given for the ‘vector’ field which appears in this ordinary divergence.