Abstract
In previous papers of this series the stability of hierarchical many-body dynamical systems has been considered in terms of parameters which are a measure of the perturbation imposed on the disturbed Keplerian orbit of each member of a system by the other bodies present.
If these parameters are small enought then the initial hierarchical order will be undisturbed for some time i.e. the status quo will be maintained and to that extent stability will exist. In the light of this criterion the appropriate parameters for the general four-body problem are considered. Two distinct hierarchical arrangments of four-body systems are possible; these are classifid and an examination of the relevant stability parameters is made in each case.
It is shown how regions may be determined within which real four-body systems can exist and may be stable. It is also shown how the various types of possible systems, (e.g.,Star-Star-Star-Star, Star-Planet-Planet-Star, etc.) within these regions may be identified.
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References
Evans, D. S.: 1968,Quart. J. Roy. Astron. Soc. 9, 388.
Plummer, H. C.: 1918An Introductory Treatise on Dynamical Astronomy, Cambridge University Press, London.
Roy, A. E.: 1979, in V. G. Szebehely (ed.),Instabilities in Dynamical Systems, D. Reidel, Publ. Co., Dordrecht. Holland.
Walker, I. W.: 1983,Cels. Mech. 29, 149.
Walker, I. W. and Roy, A. E.: 1981,Celes. Mech. 24, 195.
Walker, I. W. and Roy, A. E.: 1983,Celes. Mech. 29, 117.
Walker, I. W., Emslie, A. G., Roy, A. E.: 1980,Celes. Mech. 22, 371.
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Walker, I.W., Roy, A.E. Stability criteria in many-body systems. Celestial Mechanics 29, 267–294 (1983). https://doi.org/10.1007/BF01229140
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DOI: https://doi.org/10.1007/BF01229140