The Unified Form of Hojman’s Conservation Law and Lutzky’s Conservation Law

Abstract

In this paper, a unified form of Hojman’s conservation law and Lutzky’s one is derived. The conserved quantity is constructed in terms of a symmetry transformation vector of the equation of motion only. The Hojman’s conservation law and the Lutzky’s one may be regarded as two special cases of this unified form. A condition is deduced to exclude trivial conserved quantities. Two simple examples are presented to illustrate the applications of the results.