Equilibrium points and central configurations for the Lennard-Jones 2- and 3-body problems
The Lennard-Jones potential is used to model the stability of small clusters of interacting particles in crystal growth, random geometry of liquids, the theory of homogeneous nucleation, the motion of stars and galaxies in the Universe, etc. Most known results about the Lennard-Jones potential are found by numerical methods. Here, an analytic approach is developed to study particular circular periodic orbits and relative equilibria in Lennard-Jones 2- and 3-body problem. The main contribution is the analysis of these periodic orbits and their relationship with the momentum of inertia of the system. The results can be useful for the study dynamical properties like relaxation of systems close to equilibrium.
scientific article; zbMATH DE number 2140054