Abstract
In this paper we prove the existence of ring-type bounded motion in an isolated system consisting of a massive point particle and a homogeneous cube. We study the case of planar motion where the particle moves in a symmetry plane of the cube and we use a rotating frame of reference with its center at the mass center of the cube and its axes coinciding with the symmetry axes of the cube. We prove that, for negative values of the total energy and properly chosen values of the total angular momentum, the relative distance of the bodies has an upper and a lower bound-i.e., the regions of possible motion lie inside an annulus around the cube (motion inside a ring or an island).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bozis, G.: 1976,Astrophys. Space Sci. 43, 355.
Bozis, G. and Michalodimitrakis, M.: 1982,Astrophys. Space Sci. 86, 377.
Loks, A. and Sergysels, R.: 1985,Astron. Astrophys. (in press).
MacMillan, W. D.: 1958,The Theory of the Potential, Dover Publ., New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Michalodimitrakis, M., Bozis, G. Bounded motion in a generalized two-body problem. Astrophys Space Sci 117, 217–225 (1985). https://doi.org/10.1007/BF00650148
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00650148