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Zero velocity hypersurfaces for the general three-dimensional three-body problem

par Sergysels, Roland
Référence Celestial Mechanics, 38, 3, page (207-214)
Publication Publié, 1986-03

Article révisé par les pairs

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Résumé :

The equation of zero velocity surfaces for the general three-body problem can be derived from Sundman's inequality. The geometry of those surfaces was studied by Bozis in the planar case and by Marchal and Saari in the three-dimensional case. More recently, Saari, 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, we also find an inequality stronger than Sundman's. The comparison with Saari's inequality is more difficult. However, our 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. © 1986 D. Reidel Publishing Company.