Related papers: Loose ends in a strong force 3-body problem
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We consider the three body problem on $S^1$ under the cotangent potential. We first construct homothetic orbits ending in singularities, including total collision singularity and collision-antipodal singularity. Then certain symmetrical…
The Newtonian restricted three-body problem involving a positive primary point mass, $m_+$, and a negative secondary point mass, $m_-$, in a circular orbit, and a positive or negative tertiary point mass, $m_3$, with $m_+ > |m_-| \gg…
We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…
The $N$-body problem with a $1/r^2$ potential has, in addition to translation and rotational symmetry, an effective scale symmetry which allows its zero energy flow to be reduced to a geodesic flow on complex projective $N-2$-space, minus a…
We shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called `flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When equality holds in this inequality, we show that all the ends…
The problem of $N$ particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some quite remarkable specific cases have been solved in one dimension, whereas higher-dimensional exactly solved systems…
In this work, we study the periodic orbits in the spatial isosceles three-body problem. These periodic orbits form a one-parameter set with a rotation angle $\theta$ as the parameter. Some new phenomenons are discovered by applying our…
Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We…
Consider a broken geodesics $\alpha([0,l])$ on a compact Riemannian manifold $(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for…
The subject is brake orbits for the 3-body problem: orbits where all velocities are zero at some instant. We extract a paradox and a mystery out of a recent database of 30 non-collision periodic brake orbits for the equal mass 3-body…
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…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
We present numerical simulations of the gravitational three-body problem, in which three particles lie at rest close to the vertices of an equilateral triangle. In the unperturbed problem, the three particles fall towards the center of mass…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral…
The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…
Using one-dimensional spin-orbital model as a typical example of quantum spin systems with richer symmetries, we study the effect of an isolated impurity on its low energy dynamics in the gapless phase through bosonization and…
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,…
Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The…