A Pedagogical Relook at Bertrand's Theorem

摘要

Bertranda??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 Bertranda??s theoremarises, including interesting scenarios in the regime ofEinsteina??s general theory of relativity.