Abstract
In this paper we discuss some aspects of the isosceles case of the rectilinear restricted problem of three bodies, where two primaries of equal mass move on rectilinear ellipses, and the particle is confined to the symmetry axis of the system. In particular, the behaviour near a collision of the primaries and also near a collision of all three bodies is investigated. It is shown that this latter singularity is a triple collision in the sense of Siegel's theory. Furthermore, asymptotic expansions for the particle's motion during a parabolic and a hyperbolic escape are derived.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Siegel, C. L.: 1941,Ann. Math. 42, 127–168 =Gesammelte Abhandlungen II, 169–210.
Sperling, H. J.: 1969,Celes. Mech. 1, 210–212.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Waldvogel, J. The rectilinear restricted problem of three bodies. Celestial Mechanics 8, 189–198 (1973). https://doi.org/10.1007/BF01231413
Issue Date:
DOI: https://doi.org/10.1007/BF01231413