Computer simulations of rotating systems of few particles bound by gravitation

摘要

The shapes of rotating drops of liquid bound by gravitation is a classical subject of study. Inspired by this classical theory, we have simulated numerically a related problem, the rotating rigid configurations of a finite number of point particles. Two particles at a distance r have a long range attractive potential -1/r and a short range repulsive potential 1/r(2) preventing collapse. We take the angular momentum to be conserved, but not the energy. This system has a variable density, unlike the classical liquid drops. When the number of particles is small, it is more rigid than a liquid drop, implying that many different stable equilibrium configurations may exist with the same angular momentum but different energies. When the number of particles becomes large, our system should resemble a self-gravitating polytropic gas. We present here the results of a preliminary study with only 3, 4, and 5 particles. The methods used could be applied to the study of rotating molecules.