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Eur. J. Phys. 21 No 5 (September 2000) 465-482
PII: S0143-0807(00)14581-7

Regular Keplerian motions in classical many-body systems

Eugene I Butikov
St Petersburg State University, St Petersburg, Russia

E-mail: butikov@spb.runnet.ru

Received 30 May 2000

Abstract. A clear and simple physical approach to the explanation of exact particular solutions of the classical many-body problem is suggested. When the motion of individual bodies coupled by mutual gravitational forces in a many-body system occurs along conic sections, each body can be treated as moving not under the pull of the other moving bodies, but rather under a stationary central inverse-square gravitational field. These solutions describing possible amazingly simple (Keplerian) many-body motions are illustrated by computer simulations. Some pedagogical and philosophical aspects of the problem are discussed.


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