Generalized Non-Standard Lagrangians

Generalized Non-Standard Lagrangians 

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Niyousha Davachi and Zdzislaw E. Musielak

Department of Physics, The University of Texas at Arlington, Arlington, TX, 76019


A generalized Lagrange formalism is developed for Ordinary Differential Equations (ODE) with the special function solutions1. The formalism is based on non-standard Lagrangians, which represent a novel family of Lagrangians. It is shown that the Euler-Lagrange equation needs to be supplemented with an auxiliary condition to retrieve the original equation - this is a new phenomenon in the calculus of variations.

1. G.M. Murphy, Ordinary Differential Equations and Their Solutions, New York: Dover Publication, Inc., 2011.