Related papers: The Investigation of Stationary Points In Central …
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…
A previous work introduced pair space, which is spanned by the center of mass of a system and the relative positions (pair positions) of its constituent bodies. Here, I show that in the $N$-body Newtonian problem, a configuration that does…
Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
In the framework of restricted five bodies problem, the existence and stability of the libration points are explored and analysed numerically, under the effect of non--isotropic mass variation of the fifth body (test particle or…
We have numerically computed planar central configurations of $n=1000$ bodies of equal masses. A classification of central configurations is proposed based on the numerical value of the complexity, $\mathcal{C}$. The main result of our work…
We study the problem of planar central configurations with $N$ heavy bodies and $k$ bodies with arbitrary small masses. We derive the equation which describe the limit of light masses going to zero, which can be seen as the equation for…
Planar central configurations can be seen as critical points of the reduced potential or solutions of a system of equations. By the homogeneity and invariance of the potential with respect to SO(2), it is possible to see that the…
We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for n = 5 and 6, with equal masses. For each central configuration we give a full list of its euclidean symmetries. For all masses…
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…
We describe all countable particle systems on $\mathbb{R}$ which have the following three properties: independence, Gaussianity and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson…
In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of…
We provide a computer-assisted proof of the exact count of classes of central configurations for five bodies for several sets of mass values that are exceptional from the point of view of the finiteness results of Albouy and Kaloshin in the…
A stochastic optimization algorithm for analyzing planar central and balanced configurations in the $n$-body problem is presented. We find a comprehensive list of equal mass central configurations satisfying the Morse equality up to $n=12$.…
In this paper, the compressible quantum model with the given mass source and the external force of general form in three-dimensional whole space is considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the existence and…
The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. This is done including both Poynting-Robertson effect and stellar wind. The solutions are stationary in semimajor…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the third particle can orbit and the domain of basins of convergence linked…
Central configurations play a fundamental role in the Newtonian $n$-body problem, as they give rise to motions in which the configuration evolves while preserving its shape up to rotation and scaling. These include relative equilibria,…