Nonstandard variational calculus with applications to classical mechanics. 1. An existence criterion

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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.
Original languageEnglish
Pages (from-to)1569-1592
Number of pages24
JournalInternational Journal of Theoretical Physics
Volume38
Publication statusPublished - 1999

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Physics and Astronomy (miscellaneous)

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