Related papers: A New Class of Solvable Many-Body Problems
We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge-invariant model describing the motion of nonrelativistic particles. When we use…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
We give a surface integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current multipole moments. The derivation requires…
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
Consider the time-periodic flow of an incompressible viscous fluid past a body performing a rigid motion with non-zero translational and rotational velocity. We introduce a framework of homogeneous Sobolev spaces that renders the resolvent…
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…
This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…
In the context of the Newtonian N-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration. Moreover, it is a free time minimizer of the respective…
Second order Newton equations of motion for a radiating particle are presented. It is argued that the trajectories obeying them also satisfy the Abraham-Lorentz-Dirac (ALD) equations for general 3D motions in the non-relativistic and…
We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
We present a framework for general relativistic N-body simulations in the regime of weak gravitational fields. In this approach, Einstein's equations are expanded in terms of metric perturbations about a Friedmann-Lema\^itre background,…
In the Newtonian limit of $f(R)$ gravity, for an isolated self-gravitating system consisting of $N$ extended fluid bodies, the inter-body dynamics are studied by applying the symmetric and trace-free formalism in terms of irreducible…
We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body…
We study the Newton-like problem of minimal resistance for a two-dimensional body moving with constant velocity in a homogeneous rarefied medium of moving particles. The distribution of the particles over velocities is centrally symmetric.…