Related papers: N-body linear force law allowing analytic solution…
The attractive and repulsive linear Hookean form of gravity is known to allow for analytic solutions to N-body systems for arbitrary masses and initial conditions. This linear system is very well suited for use in the advanced undergraduate…
The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All…
We consider the problem of how to determine the force laws in an amorphous system of interacting particles. Given the positions of the centers of mass of the constituent particles we propose a new algorithm to determine the inter-particle…
Pairwise forces between particles in cosmological N-body simulations are generally softened to avoid hard collisions. Physically, this softening corresponds to treating the particles as diffuse clouds rather than point masses. For particles…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
In this paper we consider a system of $N$ particles on the real line evolving according to Newton's law, interacting through a singular (repulsive) force deriving from the potential $\frac{|x|^{1-\alpha}}{1-\alpha}$ with $\alpha \in…
We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the…
We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto…
The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for…
According to Newton's law of gravitation the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter all three of these are equal and positive. We consider here…
In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of…
We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
The problem of $N$ particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some quite remarkable specific cases have been solved in one dimension, whereas higher-dimensional exactly solved systems…
We study a nonequilibrium Langevin many-body system containing two 'test' particles and many 'background' particles. The test particles are spatially confined by a harmonic potential, and the background particles are driven by an external…
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…
From the principle of maximum entropy for a closed system in thermal equilibrium, for the first instance a clear relation is shown to exist between total entropy S (in terms of arrangements of particles) and the classical expression for the…
In this paper we consider the conformal dynamics for a system of $N$ interacting relativistic massless particles. A detailed study is done for the case of two-particles, with a particular attention to the symmetries of the problem. In fact,…