Related papers: Computing collinear 4-Body Problem central configu…
We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with T(d) symmetry are analyzed with respect to the energy spectrum, transition form…
For 3-body problem with any given masses $m_1, \,m_2,\,m_3>0$, there exist only Eulerian collinear central configuration and Lagrangian equilateral-triangle central configuration, and in this paper, for planar 3-body problem, we prove that…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
The central component of a polygon triangulation is defined as the triangle or diameter that contain its geometric center. More generally, every polygon dissection contains a central component. Using this notion, we derive new recurrences…
We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the…
Calculation of the centre of mass of a group of particles in a periodically-repeating cell is an important aspect of chemical and physical simulation. One popular approach calculates the centre of mass via the projection of the individual…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
A polyhedral approximation of a convex body can be calculated by solving approximately an associated multiobjective convex program (MOCP). An MOCP can be solved approximately by Benson type algorithms, which compute outer and inner…
We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…
We present a practical method to solve the proton-deuteron scattering problem at energies above the three-body breakup threshold, in which we treat three-body integral equations in coordinate space accommodating long-range proton-proton…
It is clear that matter is dominant in the Universe compared to antimatter. We call this problem baryon asymmetry. The baryon asymmetry is experimentally determined by both cosmic microwave background and big bang nucleosynthesis…
Every polyhedral cone can be described either by its facets or by its extreme rays. Computation of one description from the other is a problem that can be very complex, i.e. one encounter the combinatorial explosion. We present here several…
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…
We present a novel solution to the camera pose estimation problem, where rotation and translation of a camera between two views are estimated from matched feature points in the images. The camera pose estimation problem is traditionally…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters…
There is a very extensive literature dealing with convex polytopes from the standpoints of combinatorics and numerical analysis. By contrast, the current paper adopts an alternative viewpoint that regards a polytope as an autonomous space…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…