Using the framework of nonstandard analysis, I find the discretized version of the Euler-Lagrange equation for classical dynamical systems and discuss the existence of an extremum for a given functional in variational calculus. Some results related to the Cauchy existence theorem are obtained and discussed with various examples.
Bagarello, F. (1999). Nonstandard variational calculus with applications to classical mechanics. 1. An existence criterion. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 38(5), 1569-1592 [10.1023/A:1026661620598].
Nonstandard variational calculus with applications to classical mechanics. 1. An existence criterion
BAGARELLO, Fabio
1999-01-01
Abstract
Using the framework of nonstandard analysis, I find the discretized version of the Euler-Lagrange equation for classical dynamical systems and discuss the existence of an extremum for a given functional in variational calculus. Some results related to the Cauchy existence theorem are obtained and discussed with various examples.
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