Redefinition of position variables and the reduction of higher-order Lagrangians

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Abstract
Single‐time Lagrangians are treated in this paper, describing the dynamics of systems of point particles, which are given as formal power series in some ordering parameter and which may contain higher time derivatives in all terms but the leading one. An efficient method for eliminating the higher time derivatives directly on the Lagrangian level is presented. This method clarifies the meaning of using the lower‐order equations of motion in higher‐order terms in a Lagrangian. The method consists of an iterative use of ‘‘contact’’ transformations in the jet prolongation of the extended configurations space and is called ‘‘the method of redefinition of position variables.’’ Several examples from electrodynamics and relativistic gravity are treated explicitly.