Related papers: Central configurations of the spatial seven-body p…

Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another…

An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…

The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…

Geometrical properties of three-body orbits with zero angular momentum are investigated. If the moment of inertia is also constant along the orbit, the triangle whose vertexes are the positions of the bodies, and the triangle whose…

The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…

The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a consistent system of hex equations, two variables on…

We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…

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…

In the context of classical or quantum many-body problems involving identical bodies, a linear change of coordinates can be constructed with the properties that it includes the center-of-mass as one of the new coordinates and preserves the…

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…

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…

In this paper we study spiderweb central configurations for the $N$-body problem, i.e configurations given by $N=n \times \ell+1$ masses located at the intersection points of $\ell$ concurrent equidistributed half-lines with $n$ circles and…

The axisymmetric five-body problem with the concave configuration has been studied numerically to reveal the basins of convergence, by exploring the Newton-Raphson iterative scheme, corresponding to the coplanar libration points (which act…

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…

This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to…

For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result…

The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…

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…

We show existence of centrally symmetric maps on surfaces all of whose faces are quadrangles and pentagons for each orientable genus $g \geq 0$. We also show existence of centrally symmetric maps on surfaces all of whose faces are hexagons…

For the curved n-body problem, we show that the set of ordinary central configurations is away from most singular configurations in H^3, and away from a subset of singular configurations in S^3. We also show that each of the n!/2 geodesic…