Computer Science
Scientific paper
Mar 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..38..207s&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 38, March 1986, p. 207-214.
Computer Science
4
Surface Geometry, Three Body Problem, Three Dimensional Bodies, Velocity Distribution, Celestial Mechanics, Inequalities, Kinetic Energy, Rotating Bodies
Scientific paper
The equation of zero velocity surfaces for the general three-body problem can be derived from Sundman's inequality. The geometry of the surfaces was studied by Bozis (1976) in the planar case and by Marchal and Saari (1975) in the three-dimensional case. More recently, Saari (1984), using a geometrical approach, has found an inequality stronger than Sundman's. Using Bozis' algebraic method, and a rotating frame which does not take into account entirely the rotation of the three-body system, an inequality stronger than Sundman's is found. The comparison with Saari's inequality is more difficult. However, the present result can be expressed in four-dimensional space, and the regions where motion is allowed can be seen (numerically) to lie 'inside' those obtained by the use of Sundman's inequality.
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