Author： Vidal Claudio
Publisher： Springer Publishing Company
ISSN： 0923-2958
Source： Celestial Mechanics and Dynamical Astronomy, Vol.71, Iss.1, 1998-05, pp. : 15-33
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
We consider four bodies in space with same masses forming two binaries, each one symmetric with respect to a fixed axis and moving under Newtonian gravitation in opposite directions about this axis. It is given a direct proof that all singularities of this model are due to collisions, and it is proved that the singularities due to simultaneous double collisions are regularizable.The set of equilibrium points on the total collision manifold is studied as well as the possible connections among them. We show that the set of initial conditions on a given energy surface going to quadruple collision is a union of twenty submanifolds: twelve of them have dimension 2 and the others have dimension 3. Similarly for ejection orbits from quadruple collision.
Related content
Access to resources
Recommend
Quaternions and the rotation of a rigid body
By Arribas M. Elipe A. Palacios M.
Celestial Mechanics and Dynamical Astronomy, Vol. 96, Iss. 3-4, 2006-11 ,pp. :