Generalized Non-Standard Lagrangians

Abstract

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.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.