Related papers: Unchained polygons and the N-body problem
We consider the limit $N\to +\infty$ of $N$-body type problems with weak interaction, equal masses and $-\sigma$-homogeneous potential, $0<\sigma<1$. We obtain the integro-differential equation that the motions must satisfy, with limit…
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…
Examples are given of solutions of the planar N-body problem which remain the same for at least two systems of masses with the same sum and same center of mass. The least value of N achieved up to now with this property is 474, a number…
Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
We study the existence of families of periodic solutions in a neighbourhood of a symmetric equilibrium point in two classes of Hamiltonian systems with involutory symmetries. In both classes, involutions reverse the sign of the Hamiltonian…
We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length…
We obtain a new exact equilibrium solution to the N-body problem in a one-dimensional relativistic self-gravitating system. It corresponds to an expanding/contracting spacetime of a circle with N bodies at equal proper separations from one…
Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…
We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
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…
The paper investigates a generalization of the classical Sitnikov problem, concentrating on the movement of a satellite along the Z-axis as it interacts with $n$ primary bodies in periodic motion. It establishes the existence of an infinite…
We revisit the r\^{o}le of discreteness and chaos in the dynamics of self-gravitating systems by means of $N$-body simulations with active and frozen potentials, starting from spherically symmetric stationary states and considering the…
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, $d\ge 2$, the simplest possible periodic solutions are provided by circular relative equilibria, (RE) for short, namely solutions in which each body…
Equations of motion of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles…
The validity of Sundman-type asymptotic estimates for collision solutions is established for a wide class of dynamical systems with singular forces, including the classical $N$--body problems with Newtonian, quasi--homogeneous and…
In the framework of the spatial circular Hill three-body problem we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbit families. The extensive collection of families within this…
The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the…