A brief discussion on variational principle and some applications

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  • 1. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China; 
    2. School of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028043, China

Received date: 2023-01-14

  Revised date: 2023-02-28

  Online published: 2023-11-06

Abstract

 The variational principle is introduced, and its Euler-Lagrange equation for the minimum of variational problems in the setting of one dimension is described. Then, the corresponding specific expression of these Euler-Lagrange equations for taking a geodesic line, geodesic curve, Brachistochrone and isoperimetric problems are deduced as examples, respectively. The solutions of the corresponding original problems are obtained and the relevant generalizations are given.

Cite this article

ZHENG Shen-zhou, YU Hai-yan . A brief discussion on variational principle and some applications[J]. College Physics, 2023 , 42(10) : 1 . DOI: 10.16854/j.cnki.1000-0712.230014

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