Take a look at this white dot tracking the hips.
(The hips are not exactly the center gravity like the center of a bouncing ball is, but they are typically not far from it and easy to follow)
Compare their path to the dots tracking my hips in the video of the one-legged hop (linked to earlier), especially regarding the start, where I begin from a standstill, and the end where I finish at a standstill, much like what you are trying to do here.