A Partial Proof of Bertrand's Theorem

Honors College Thesis

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

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Attribute Name	Values
Creator	Musgrove, John F.
Abstract	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
License	All rights reserved
Resource Type	Honors College Thesis
Date Issued	2020-05-31
Degree Level	Bachelor's
Degree Name	Honors Bachelor of Science (H.B.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2020
Advisor	De Leenheer, Patrick
Committee Member	Thomann, Enrique Faridani, Adel
Non-Academic Affiliation	Oregon State University. Honors College
权利声明	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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