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Stable and Minimum Energy Configurations in the Spherical, Equal Mass Full 4-Body Problem

D.J. Scheeres1

Department of Aerospace Engineering Sciences, The University of Colorado. E-mail:

Computer Modeling in Engineering & Sciences 2016, 111(3), 203-227.


The minimum energy and stable configurations in the spherical, equal mass full 4-body problem are investigated. This problem is defined as the dynamics of finite density spheres which interact gravitationally and through surface contact forces. This is a variation of the gravitational n-body problem in which the bodies are not allowed to come arbitrarily close to each other (due to their finite density), enabling the existence of resting configurations in addition to orbital motion. Previous work on this problem has outlined an efficient and simple way in which the stability of configurations in this problem can be defined. This methodology is applied to the 4-body problem, where we find multiple resting equilibrium configurations and outline the stability of a number of these. The study of these configurations is important for understanding the mechanics and morphological properties of small rubble pile asteroids. These results can also be generalized to other configurations of bodies that interact via field potentials and surface contact forces.


Cite This Article

Scheeres, D. (2016). Stable and Minimum Energy Configurations in the Spherical, Equal Mass Full 4-Body Problem. CMES-Computer Modeling in Engineering & Sciences, 111(3), 203–227.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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