Physics
Scientific paper
Jun 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993acasn..34..202f&link_type=abstract
Acta Astronomica Sinica (ISSN 0001-5245), vol. 34, no. 2, p. 208-217
Physics
Attraction, Field Theory (Physics), Many Body Problem, Celestial Mechanics, Two Body Problem
Scientific paper
It is impossible to obtain the general solution of the N-body problem, so searching its particular solutions is of great interest. Up to now, homographic solutions are the only known analytical particular solutions of the N-body problem. Under the law of gravitation, a lot of results on homographic solutions have already been obtained. In this paper the same topic is discussed under the general attraction. The existence of homographic solutions of the N-body problem is verified, and the way which leads to obtaining certain types of homographic solutions is indicated. Basic properties of the solutions, such as the relations between the dynamical quantities and the initial conditions are presented. Furthermore, we proved that, for k is not equal to 3, if a homographic solution is not planar, it must be homothetic. Finally, we showed that along each homographic solution, motion of any individual mass point observes the same rules as the ones observed by mass points of a certain two-body system.
Fu Yan-Ning
Sun Yi-Sui
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