Related papers: A Separating Surface for Sitnikov-like n+1-body Pr…
In this paper we address a $n+1$-body gravitational problem governed by the Newton's laws, where $n$ primary bodies orbit on a plane $\Pi$ and an additional massless particle moves on the perpendicular line to $\Pi$ passing through the…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions in dynamical systems, Princeton University Press, 1973). We…
We consider the planar restricted $N$-body problem where the $N-1$ primaries are assumed to be in a central configuration whereas the infinitesimal particle escapes to infinity in a parabolic orbit. We prove the existence of transversal…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
We show the existence of some infinite families of periodic solutions of the planar Newtonian n-body problem --with positive masses-- which are symmetric with respect to suitable actions of finite groups (under a strong--force assumption,…
We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three…
We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…
The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
We generalize the Newtonian n-body problem to spaces of curvature k=constant, and study the motion in the 2-dimensional case. For k>0, the equations of motion encounter non-collision singularities, which occur when two bodies are antipodal.…
We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show that the lack of uniformity in the…
We report on the results of a study of the motion of a four particle non-relativistic one-dimensional self-gravitating system. We show that the system can be visualized in terms of a single particle moving within a potential whose…
We use variational minimizing methods to study spatial restricted N+1-body problems with a zero mass moving on the vertical axis of the moving plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which…
In this talk I describe recent joint works with R.Schoen and with G.Gibbons and R.Schoen which prove the non-existence of certain asymptotically flat, stationary solutions of the Einstein equations with more than one body. The basic…
The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…