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ERIC Number: EJ931776
Record Type: Journal
Publication Date: 2011-Jul
Pages: 9
Abstractor: As Provided
Reference Count: 10
ISBN: N/A
ISSN: ISSN-0143-0807
Possible Potentials Responsible for Stable Circular Relativistic Orbits
Kumar, Prashant; Bhattacharya, Kaushik
European Journal of Physics, v32 n4 p895-903 Jul 2011
Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In this paper an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in the presence of a force which is proportional to the negative of the displacement of the particle from the potential centre. (Contains 1 footnote.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A