Related papers: Stability of the regular $n$-gon rotating equilibr…
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…
It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter $\beta$ and on the eccentricity $e$ of the orbit. We consider only the circular case ($e…
In this paper we characterize all the solutions of the three body problem on which one body with mass $m_1$ remains in a fixed line and the other two bodies have the same mass $m_2$. We show that all the solutions with negative total energy…
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…
In this paper we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. Firstly, in the case the potential is a homogeneous function of degree $-a$, we find that any relative equilibrium of…
For the curved n-body problem in S^3, we show that a regular polygonal configuration for n masses on a geodesic is an equilibrium configuration if and only if n is odd and the masses are equal. The equilibrium configuration is associated…
In this paper we study the linear stability of selfinteracting boson stars in the nonrelativistic limit of the Einstein-Klein-Gordon theory. For this purpose, based on a combination of analytic and numerical methods, we determine the…
We give a computer assisted proof of the full listing of central configuration for $n$-body problem for Newtonian potential on the plane for $n=5,6,7$ with equal masses. We show all these central configurations have a reflective symmetry…
Motivated by Xia-Zhou's recent work on applying symmetry groups to the N-body problem, we will study relative equilibria of the equilateral triangle and the square configurations under $\alpha$-homogeneous and quasi-homogeneous potentials…
In this new era of gravitational wave astrophysics, observations have indicated the likely existence of black holes with significant spin. In order to better understand the potential imprint orbital dynamics have on the multi-messenger…
We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…
In the $2$-dimensional $n$-body problem, $n\ge 3$, in spaces of constant curvature, $\kappa\ne 0$, we study polygonal homographic solutions. We first provide necessary and sufficient conditions for the existence of these orbits and then…
We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically…
The closed relativistic string carrying a point-like mass in the space with nontrivial geometry is considered. For rotational states of this system (resulting in non-trivial Regge trajectories) the stability problem is solved. It was shown…
The regular $n$-gon elliptic relative equilibrium (ERE) is a Kepler homographic solution generated by the regular $n$-gon central configuration, and its linear stability depends on the eccentricity $\mathfrak{e}\in[0,1)$. While Moeckel…
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.…
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 use a systolic N-body algorithm to evaluate the linear stability of the gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude greater than in previous experiments. For the first time, a clear ~ln N-dependence of…
For the linear baryon string model with three massive points (three quarks) connected sequentially by the relativistic strings the initial-boundary value problem is stated and solved in general. This problem implies defining a classical…
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter $\bb=27(m_1m_2+m_2m_3+m_3m_1)/(m_1+m_2+m_3)^2\in [0,9]$…