Classical Particle in a Coulomb-Like Radial Potential

This Demonstration shows the negative energy trajectories of a point mass moving in the radially symmetric potential U(x,y,z)-(x^{2}+y^{2}+z^{2})^{-α/2}. Due to the radial symmetry the point mass moves in a two-dimensional plane perpendicular to the angular momentum vector.

The case of corresponds to the Coulomb potential, where negative energy trajectories are periodic. For , all the negative energy trajectories go through the origin.