The Investigation of Stationary Points In Central Configuration Dynamics
Abstract
A system of N points, each having mass m, and a central mass M forming a planar central configuration, is considered. The equations of motion of a test particle are given and compared using different coordinates. For large values of N, even or odd, the equations are given too. The method used for the computation of some relevant sums can be important for practical applications. It is shown that the stationary solutions (libration points) can be determined from an algebraic equation of 5th degree. If the mass of the particles is large, the outer libration points disappear. For the inner libration points the limit minimal distance has been detected. If m=M is small the solution obtained for the libration has as limit a solution similar to the for 3body collinear points. We have also constructed a central configuration with 2N + 1 bodies, in which N new particles, each of mass m1= m, are placed at the libration points of our first system.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505404
 arXiv:
 arXiv:math/0505404
 Bibcode:
 2005math......5404R
 Keywords:

 Mathematics  Dynamical Systems;
 70F16
 EPrint:
 14 pages with 3 figures, preprint version