Related papers: Computing collinear 4-Body Problem central configu…
In this article is given a simple expression for the \textit{ center of mass} for a system of material points in a two-dimensional surface of constant negative Gaussian curvature. Using basic techniques of Geometry, an expression in…
We study the multichannel scattering in the classical three-body system and show that the problem can be formulated as a motion of the point mass on a curved hyper-surface of the energy of the body-system. It is proved that the local…
The four-body equations of Alt, Grassberger and Sandhas are solved for $\nH$ scattering at energies below three-body breakup threshold using various realistic interactions including one derived from chiral perturbation theory. After partial…
We consider the planar central configurations of the Newtonian $\kappa n$-body problem consisting in $\kappa$ groups of $n$-gons where all $n$ bodies in each group have the same mass, called $(\kappa, n)$-crown. We study the location and…
Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to…
A simple method is proposed for determining the masses of new particles in collider events containing a pair of decay chains (not necessarily identical) of the form Z -> Y+1, Y -> X+2, X -> N+3, where 1,2 and 3 are visible but N is not.…
An alternative approach to the Standard Model is outlined, being motivated by the increasing theoretical and experimental difficulties encountered by this model, which furthermore fails to be unitary. In particular, the conceptual…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which…
The concept of centre of mass of two particles in 2D spaces of constant Gaussian curvature is discussed by recalling the notion of "relativistic rule of lever" introduced by Galperin [Comm. Math. Phys. 154 (1993), 63--84] and comparing it…
We show that any polyhedron forming a topological ball with an even number of quadrilateral sides can be partitioned into O(n) topological cubes, meeting face to face. The result generalizes to non-simply-connected polyhedra satisfying an…
A method is proposed for determining the masses of the new particles N,X,Y,Z in collider events containing a pair of effectively identical decay chains Z to Y+jet, Y to X+l_1, X to N+l_2, where l_1, l_2 are opposite-sign same-flavour…
A toric arrangement is an arrangement of subtori of codimension one in a real or complex torus. The poset of layers is the set of connected components of non-empty intersections of these subtori, partially ordered by reverse inclusion. In…
In this paper,we show the existence of a class of 6-body central configurations with two isosceles triangles; which are congruent to each other and keep some distance.We also study the necessary conditions about masses for the bodies which…
It is well known that the three-body problem has few analytical solutions in certain symmetrical constraints; the Lagrangian triangular solution is one of them. This triangular solution has been revisited by R.Broucke and H.Lass in 1971,…
We prove the existence of a number of smooth periodic motions $u_*$ of the classical Newtonian $N$-body problem which, up to a relabeling of the $N$ particles, are invariant under the rotation group ${\cal R}$ of one of the five Platonic…
We consider the Hill four-body problem where three oblate, massive bodies form a relative equilibrium triangular configuration, and the fourth, infinitesimal body orbits in a neighborhood of the smallest of the three massive bodies. We…
We discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
Molecular Mechanics describes molecules as particle configurations interacting via classical potentials. These {\it configurational energies} usually consist of the sum of different phenomenological terms which are tailored to the…
In this work, we perform a first study of basic invariant sets of the spatial Hill's four-body problem, where we have used both analytical and numerical approaches. This system depends on a mass parameter mu in such a way that the classical…