A Simple Charged Three-Body Problem

A Simple Charged Three-Body Problem

Dedicated to Paul Blanchard on the occasion of his sixtieth birthday. Abstract: The dynamics of a simple model of three charged bodies interacting under an inverse square electrostatic force is presented. The model may be viewed as an alternative to the pendulum, the standard model of a periodically forced and damped nonlinear oscillator.

Qualitative Study of a Charged Restricted Three–body Problem

We characterize the global flow of the restricted threebody problem in which we have two mass points of equal masses m1 = m2 > 0 and equal charge q1 = q2 moving on a straight line under Newtonian and Coulombian forces with their centre of mass being fixed at the origin of coordinates and the third mass point with infinitesimal mass, is moving on the straight line perpendicular to the line of mo...

A Trilinear Three-Body Problem

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton’s inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful m...

Three-body forces between charged colloidal particles.

Within nonlinear Poisson-Boltzmann theory we calculate the pair and triplet interactions between charged colloidal spheres, specifically in the nonlinear regime of low salt concentrations and high charges. We find repulsive pair interactions and attractive triplet interactions. Within a van der Waals-like mean-field theory we estimate in which parameter regime a gas-liquid coexistence is to be ...

Three - Body Problem