Once the gymnasts can make their front hip circles to the support by themselves, two important goals are to minimize bending of the arms when coming back to the support and to begin connecting their font hips circles to a nice cast.
This next gymnast demonstrates a nice starting hollow body position with the bar correctly placed approximately at mid-thighs and a fair cast to horizontal. Check in this slow motion example how when the body starts falling down by gravity, the gymnasts pikes to accelerate the circle around. At that same time, she re-shifts her grip to come back to the support ready for the cast. Look again how she raises her center of mass to speed up her circle initiation with the extra pike down when the body is already falling by gravity. Observe now the quick hands strip shifting right when the body is going to pike.
Still Frame 1: Center of mass, hollow body, with bar around mid thighs.
Still Frame 2: Hollow body leans forward into fall, arms pressure legs against the bar. Still Frame 3: Hollow body falling down by gravity, bar resting on legs quick hands shifting begins.
Still Frame 4: Final cast moves up with a subtle tight arch.
Still Frame 6: By the horizontal, the gymnast has changed her body shape to a hollow, elbows are locked with the shoulders in front of the vertical line.
Once more, search for some of the technical details at regular speed.