| Abstract: |
| We consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogous to Newton`s inverse square law. Viewing the curvature of space -- or equivalently the distance between the bodies -- as a small parameter, the reduced equations of motion may be viewed as a small perturbation of an integrable system: the Kepler problem. We take action-angle coordinates for this unperturbed system in order to average the perturbing terms and shed light on the curvature effects on the two-body dynamics. |
|