Abstract
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.
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References
Bozis, G.: 1976, ‘Zero Velocity Surfaces for the General Planar Three-Body Problem’,Astrophys. Space Sci. 43, 355–368.
Marchal, C. and Saari, D. G.: 1975, ‘Hill Regions for the General Three-Body Problem’,Celes. Mech. 12, 115–129.
Pars, L. S.: 1965,A Treatise on Analytical Dynamics, Wiley, New York.
Saari, D. G.: 1984, ‘From Rotations and Inclinations to Zero Configurational Velocity Surfaces’,Celes. Mech. 33, 299–318.
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Sergysels, R. Zero velocity hypersurfaces for the general three-dimensional three-body problem. Celestial Mechanics 38, 207–214 (1986). https://doi.org/10.1007/BF01231106
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DOI: https://doi.org/10.1007/BF01231106