Central Configurations and a Theorem of Palmore
Abstract
The concept of central configuration is important in the study of total collisions or the relative equilibrium state of a rotating system in the Nbody problem. However, relatively few such configurations are known. Aided by a new global optimizer, we have been able to construct new families of coplanar central configurations having particles of equal mass, and extend these constructions to some configurations with differing masses and the noncoplanar case. Meyer and Schmidt had shown that a theorem of Palmore concerning coplanar central configurations was incorrect for N equal masses where 6 ⩽ N ⩽ 20 but presented a simple analytic argument only for N = 6. Using straightforward analytic arguments and inequalities we also disprove this theorem for 2N equal masses with N ⩾ 3.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 December 1990
 DOI:
 10.1007/BF00049389
 Bibcode:
 1990CeMDA..48..347S
 Keywords:

 Equations Of Motion;
 Gravitational Constant;
 Many Body Problem;
 Computational Astrophysics;
 Equilibrium Equations;
 Astrophysics