Related papers: On the centered co-circular central configurations…
General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…
Given $n$ point masses turning in a plane at a constant speed, this paper deals with the global bifurcation of periodic solutions for the masses, in that plane and in space. As a special case, one has a complete study of n identical masses…
We consider a one-dimensional, trapped, focusing Bose gas where $N$ bosons interact with each other via both a two-body interaction potential of the form $a N^{\alpha-1} U(N^\alpha(x-y))$ and an attractive three-body interaction potential…
We compute binding energies and root mean square radii for weakly bound systems of $N=4$ and $5$ identical bosons. Ground and first excited states of an $N$-body system appear below the threshold for binding the system with $N-1$ particles.…
The dynamics of the pseudo-Newtonian restricted four-body problem has been studied in the present paper, where the primaries have equal masses. The parametric variation of the existence as well as the position of the libration points are…
This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schr\"odinger equation for these systems confined in an harmonic…
In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass.…
We solve the equation of the equilibrium of the gravitating body, with a polytropic equation of state of the matter $P=K\rho^{\gamma}$, with $\gamma=1+1/n$, in the frame of the Newtonian gravity, with non-zero cosmological constant…
In this article we introduce a general definition of the concept of center of an $n$-gon, for $n\geq 3$, generalizing the idea of C. Kimberling for triangle. We define centers associated to functions instead of to geometrical properties. We…
We prove that positive elliptic-elliptic rotopulsator solutions of the $n$-body problem in spaces of constant Gaussian curvature that move on Clifford tori of nonconstant size either lie on great circles, or project onto regular polygons.…
This paper proposes new symmetries (the body-centred cubic periodic symmetries) beyond the standard model. Using a free particle expanded Schrodinger equation with the body-centred cubic periodic symmetry condition, the paper deduces a full…
Three-body and n-body problems in celestial mechanics are age-old and challenging puzzles. In recent years, several breakthroughs are made in finding periodic orbits for three-body problem. And Bohua Sun proposed a conjecture on Kepler's…
The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schr\"odinger equation in a harmonic potential proposed recently [ J. J. Garc\'{\i}a-Ripoll, V. M. P\'erez-Garc\'{\i}a, and V.…
We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three…
Let $q_{1}$,...,$q_{n}$ be the position vectors of the point masses of the curved $n$-body problem. Consider any positive elliptic-elliptic rotopulsator solution…
The number of faces of the convex hull of $n$ independent and identically distributed random points chosen on the boundary of a smooth convex body in $\mathbb{R}^d$ is investigated. In dimensions two and three the number of $k$-faces is…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
A system of N points, each having mass m, and a central mass M forming a planar central configuration, is considered. The equations of motion of a test particle are given and compared using different coordinates. For large values of N, even…
For the curved n-body problem in S^3, we show that a regular polygonal configuration for n masses on a geodesic is an equilibrium configuration if and only if n is odd and the masses are equal. The equilibrium configuration is associated…