Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regular polygon solutions of the $ N$-body problem


Authors: L. M. Perko and E. L. Walter
Journal: Proc. Amer. Math. Soc. 94 (1985), 301-309
MSC: Primary 70F10; Secondary 15A90
MathSciNet review: 784183
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In 1772, Lagrange showed that three masses at the vertices of an equilateral triangle, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the three-body problem. In this paper it is shown that for $ N \geqslant 4,N$ masses at the vertices of a regular polygon, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the $ N$-body problem if and only if the masses are equal.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 70F10, 15A90

Retrieve articles in all journals with MSC: 70F10, 15A90


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0784183-1
PII: S 0002-9939(1985)0784183-1
Article copyright: © Copyright 1985 American Mathematical Society