Nonstandard variational calculus with applications to classical mechanics. 2. The inverse problem and more

Abstract

In this paper we continue analyzing the possible applications of nonstandard analysis to variational problems, with particular interest in classical mechanics. In particular, we adapt various techniques of numerical analysis to solve the nonstandard version of the Euler-Lagrange equation for both one-and multidimensional systems. We also start an introductory analysis of the inverse problem of the calculus of variation, identifying a class of nonstandard difference equations for which a first-order Lagrangian can be obtained.