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.
Lingua originaleEnglish
pagine (da-a)1569-1592
Numero di pagine24
RivistaInternational Journal of Theoretical Physics
Volume38
Stato di pubblicazionePublished - 1999

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existence theorems
Cauchy's integral theorem
Nonstandard Analysis
Variational Calculus
Euler-Lagrange equation
classical mechanics
Euler-Lagrange Equations
Classical Mechanics
calculus
range (extremes)
Extremum
dynamical systems
Existence Theorem
Dynamical system
Framework

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Cita questo

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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.",
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year = "1999",
language = "English",
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AB - 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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JO - International Journal of Theoretical Physics

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