相关论文: Existence of Really Perverse Central Configuration…

Examples are given of solutions of the planar N-body problem which remain the same for at least two systems of masses with the same sum and same center of mass. The least value of N achieved up to now with this property is 474, a number…

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…

A symmetric planar central configuration of the Newtonian six-body problem $x$ is called cross central configuration if there are precisely four bodies on a symmetry line of $x$. We use complex algebraic geometry and Groebner basis theory…

The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which…

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…

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…

The degeneracy of central configurations in the planar $N$-body problem makes their enumeration problem hard and the related dynamics appealing. To truly understand the bifurcations of central configurations, we should work in the FULL…

This research investigates centered co-circular central configurations in the general power-law potential $n$-body problem. Firstly, there are no such configurations when all masses are equal, except for two; secondly, unless all masses are…

We study the relationship between the masses and the geometric properties of central configurations. We prove that in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the…

For planar ($N$+1)-body ($N$\,$\geq$ 2) problem with a regular $N$-polygon, under the assumption that the ($N$+1)-th body locates at the geometric center of the regular $N$-polygon, we obtain the sufficient and necessary conditions that the…

The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged…

In this paper,we study spatial central configurations where N bodies are at the vertices of a regular N-gon $T$ and the other 4 bodies are symmetrically located on the straight line that is perpendicular to the plane that contains $T$ and…

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…

We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is…

We study the planar symmetric central configurations of the $1+4$-body problem where the symmetry axis does not contain any infinitesimal masses. Under certain assumptions we find analytically some central configurations, and also get some…

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…

In this study, we present a rigorous analytical proof of the uniqueness of central configurations for the five-body problem, assuming that all five masses are equal and positioned at the vertices of a planar polygon. We consider…

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…

Central configurations give rise to self-similar solutions to the Newtonian $N$-body problem, and play important roles in understanding its complicated dynamics. Even the simple question of whether or not there are finitely many planar…

Moeckel (1990), Moeckel and Sim\'o (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur…