Periodic Solutions of the Third Sort for Restricted Problem of Three Bodies and Their Stability

Details Periodic Solutions of the Third Sort for Restricted Problem of Three Bodies and Their Stability Periodic Solutions of the Third Sort for Restricted Problem of Three Bodies and Their Stability

Feb 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...7..156k&link_type=abstract

Celestial Mechanics, Volume 7, Issue 2, pp.156-176

Physics

3

Scientific paper

In this paper periodic solutions of the third sort for restricted problem of three bodies in the three-dimensional space are derived numerically by starting from generating solutions obtained by one of the authors (1969) and by increasing the mass-ratio of the two primaries stepwise from zero to about 1000 for 2∶1, 3∶2 and 6∶1 cases of commensurable mean motions. Periodic solutions both for circular and elliptic orbits of the primaries are obtained. The stability of the periodic solutions for the 2∶1 circular case is discussed and it is found that none of them is linearly stable.

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