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      https://www.ias.ac.in/article/fulltext/pram/094/0141

    • Keywords

       

      Calculus of variation; inverse problem; Lagrangians; linear and nonlinear systems

    • Abstract

       

      We show that the theory of self-adjoint differential equations can be used to provide a satisfactory solution of the inverse variational problem in classical mechanics. A Newtonian equation, when transformed to the self-adjoint form, allows one to find an appropriate Lagrangian representation (direct analytic representation) for it. On the other hand, the same Newtonian equation in conjunction with its adjoint provides a basis to construct a different Lagrangian representation (indirect analytic representation) for the system. We obtain the time-dependent Lagrangian of the damped harmonic oscillator from the self-adjoint form of the equation of motion and at the same time identify the adjoint of the equation with the so-called Bateman image equation with a view to construct a time-independent indirect Lagrangian representation. We provide a number of case studies to demonstrate the usefulness of the approach derived by us. We also present similar results for a number of nonlinear differential equations by using an integral representation of the Lagrangian function and make some useful comments.

    • Author Affiliations

       

      BENOY TALUKDAR1 SUPRIYA CHATTERJEE2 SEKH GOLAM ALI3

      1. Department of Physics, Visva-Bharati University, Santiniketan 731 235, India
      2. Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata 700 064, India
      3. Department of Physics, Kazi Nazrul University, Asansol 713 303, India
    • Dates

       
  • Pramana – Journal of Physics | News

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