相关论文: On Kite Central Configurations

The equations of the Newtonian $n$-body problem have a matrix form, where an $n\times n$ matrix depending on the masses and on the mutual distances appears as a factor. The $n$ eigenvalues of this matrix are real and nonnegative. In a…

Central configurations and relative equilibria are an important facet of the study of the $N$-body problem, but become very difficult to rigorously analyze for $N>3$. In this paper we focus on a particular but interesting class of…

In this work we are interested in the central configurations of the planar 1+4 body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think this problem as a…

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,…

The relative equilibria of planar Newtonian $N$-body problem become coorbital around a central mass in the limit when all but one of the masses becomes zero. We prove a variety of results about the coorbital relative equilibria, with an…

For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solutions) in which each body moves along a Keplerian orbit and the…

For any convex non-collinear central configuration of the planar Newtonian 4-body problem with adjacent equal masses $m_1=m_2\neq m_3=m_4$, with equal lengths for the two diagonals, we prove it must possess a symmetry and must be an…

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 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…

In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjecture that there exists a unique convex central configuration for any four fixed positive masses in a given order belonging to a closed domain in the mass space.…

For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration…

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…

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…

A new coordinate system on the tangent space to planar configurations is introduced to simplify some calculations on central configurations and relative equilibria in the $N$-body problem with a homogeneous potential, which includes the…

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…

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…

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…

Central configurations are fundamental equilibrium solutions of the Newtonian $n$-body problem and play a key role in understanding the structure and dynamics of gravitational systems. However, the classification and enumeration of such…

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…

We construct explicit examples of really perverse central configurations in the spatial Newtonian $N$-body problem. A central configuration is called really perverse if it satisfies the central configuration equations for two distinct mass…