• A Pedagogical Relook at Bertrand's Theorem

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/024/11/1235-1251

    • Keywords

       

      Closed bound orbits, Abel integral, Bertrand’s theorem, central force.

    • Abstract

       

      Bertrand’s theorem is one of the landmark results in the contextof the central force problem in mechanics. It leads tothe conditions for closed bound orbits. This pedagogical articleintends to motivate the teacher as well as the student toengage in a formal proof of the theorem. We overview thebasics of central forces and the Abel integral. Thereafter, weobtain the condition for closed orbits. We provide the readerwith a broad panorama of areas/topics where Bertrand’s theoremarises, including interesting scenarios in the regime ofEinstein’s general theory of relativity.

    • Author Affiliations

       

      T U Jeevitha Sanjit Das1

      1. 1VIT Chennai, School of Advanced Sciences Chennai 600127
    • Dates

       

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