Table of Contents
ISRN Astronomy and Astrophysics
Volume 2013 (2013), Article ID 281849, 15 pages
Research Article

The Restricted 2+2 Body Problem: Parametric Variation of the Equilibrium States of the Minor Bodies and Their Attracting Regions

Department of Mechanics, Faculty of Applied Mathematical and Physical Sciences, National Technical University of Athens, 15773 Athens, Greece

Received 29 November 2012; Accepted 17 December 2012

Academic Editors: P. P. Avelino, D. M. Christodoulou, M. Ding, P. A. Hughes, P. Marziani, and R. A. West

Copyright © 2013 Maria N. Croustalloudi and Tilemahos J. Kalvouridis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The restricted 2+2 body problem was stated by Whipple (1984) as a particular case of the general n + v problem described by Whipple and Szebehely (1984). In this work we reconsider the problem by studying some aspects of the dynamics of the minor bodies, such as the parametric variation of their equilibrium positions, as well as the attracting regions formed by the initial approximations used for the numerical determination of these positions. In the latter case we describe the process to form these regions, and we numerically investigate their dependence on the parameters of the system. The results in many cases show a fractal-type structure of these regions. As test problems, we use the Sun-Jupiter-binary asteroids and the Earth-Moon-dual artificial satellites systems.