> once you properly set the initial state of the ball (force=velocity=0, or any other values), then the solution becomes unique and that’s it No, you've missed

> once you properly set the initial state of the ball (force=velocity=0, or any other values), then the solution becomes unique and that’s it No, you've missed the point entirely. There are circumstances under which the solution is not unique, and the article describes such a circumstance.