Related papers: Loose ends in a strong force 3-body problem
We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time,we…
The figure eight is a remarkable solution to the Newtonian three-body problem in which the three equal masses chase each around a planar curve having the qualitative shape and symmetries of a figure eight. Here we prove that each lobe of…
This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
The Newtonian n-Body Problem is modified assuming positive inertial masses but different sign for the interacting force which is assumed with the possibility of two different signs for the gravitational masses, according to the prescription…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…
This monograph describes a Riemannian geometric reduction approach to the three-body problem. The fundamental theorems are presented in the introductory part, whereas their proofs are provided in later chapters where specific topics are…
We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical…
In this paper, an approach is developed to solve the three body problem involving masses which posses spherical symmetry. The problem dates back to the times of Poincare, and is undoubtedly one of the oldest of unsolved problems of…
We analyze the dynamics of BPS 3-vortex solutions. First, for unexcited vortices, we study the 2-dimensional moduli space of centred vortices with $y \to -y$ symmetry, and its metric. We identify the 1-dimensional subspaces describing the…
Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative…
We give a lower bound on the number of non-simple closed curves on a hyperbolic surface, given upper bounds on both length and self-intersection number. In particular, we carefully show how to construct closed geodesics on pairs of pants,…
Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…
The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double-scaling limit of the recursion relation…
We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…
We derive a general formula for the inertia tensor of a three-body system. By employing three independent Lagrange undetermined multipliers to express the vectors corresponding to the sides in terms of the position vectors of the vertices,…
We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot tend to its infimum on an unbounded sequence of states.…
The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the…