Honors College Thesis

 

A Partial Proof of Bertrand's Theorem Public Deposited

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https://ir.library.oregonstate.edu/concern/honors_college_theses/73666c15t

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  • In this paper, we provide a thorough proof of most of Bertrand's Theorem. Using Arnold's book "Mathematical methods of classical mechanics" as a backbone and calculus methods demonstrated by Jovanović in his article "A note on the proof of Bertrand's theorem," we show that for masses in a central field with bounded orbits, closed orbits are restricted to central forces obeying a power law. This paper covers a subset of all possible power laws, leading to the conclusion that only Newton's Law of gravitation and Hooke's Law provide closed, bounded orbits.
  • Key Words: Mathematics, Calculus, Physics, Classical Mechanics, Two-Body Problem
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