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      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/022/09/0847-0866

    • Keywords

       

      Variational principle, brachistochrone, tachystoptota, extremum action, Fermat’s principle, Euler–Lagrange equation.

    • Abstract

       

      The brachistochrone problem posed by Bernoulli and its solutionhighlights one of the most famous experiments in physicswhich illustrates the variational principle. This pedagogicalstudy is designed to ignite a classroom discussion on the variationalproblem. We overview the Euler–Lagrange formalismof the variational principle and obtain the solution to thebrachistochrone problem. We demonstrate the success of thevariationalmethod using brachistochronemodels which werefabricated specially for this purpose.

    • Author Affiliations

       

      P C Deshmukh1 Parth Rajauria2 Abiya Rajans2 B R Vyshakh2 Sudipta Dutta2

      1. Department of Physics, Indian Institute of Science Education and Research, Tirupati 517 507, India.
      2. Department of Physics, Indian Institute of Science Education and Research, Tirupati, Tirupati 517 507, India.
    • Dates

       

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