Related papers: Relative Equilibria in the Spherical, Finite Densi…
In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration.…
The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient…
In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…
We investigate some properties of the dynamical system of point vortices on the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint equivariant momentum map J. The relative equilibrium conditions are found and the…
We consider the $n$--body problem defined on surfaces of constant negative curvature. For the case of $n$--equal masses we prove that the hyperbolic relative equilibria with a regular polygonal shape do not exist. In particular the…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center of mass of the system with perturbed mean motion. Using analytical and numerical methods we have found…
We study relative equilibria ($RE$ in short) for three-body problem on $\mathbb{S}^2$, under the influence of a general potential which only depends on $\cos\sigma_{ij}$ where $\sigma_{ij}$ are the mutual angles among the masses. Explicit…
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.…
One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for…
We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly),…
We prove for generalisations of quasi-homogeneous $n$-body problems with center of mass zero and $n$-body problems in spaces of negative constant Gaussian curvature that if the masses and rotation are fixed, there exists, for every order of…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
We have examined the stability of triangular equilibrium points in Robes's generalised restricted three body problem. The problem is generalised in the sense that more massive primary has been taken as an oblate spheroid. We have found the…
We prove that if for the curved $n$-body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero.…
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem…
We consider the curved 4-body problems on spheres and hyperbolic spheres. After obtaining a criterion for the existence of quadrilateral configu- rations on the equator of the sphere, we study two restricted 4-body problems, one in which…
We analyze existence, stability, and symmetry of point vortex relative equilibria with one dominant vortex and N vortices with infinitesimal circulation. The dimension of the problem can be reduced by taking an infinitesimal circulation…
A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances…