Lay prone with waist on stability ball. Grasp secure anchor or bar near floor. Feet should be above floor with legs straight.
Holding firmly on anchor, extend legs upward by lifting and straightening leg as high as possible. Lower legs to original position with thighs close to stability ball. Repeat.
Since knee is initially bent significantly, hamstrings are not significantly involved. Also see Reverse Hyper-extension performed with exercise ball on bench.
Keep knees bent to make exercise easier. Also consider regular hyper-extensions or other bodyweight glute exercises.
Exercise can be made more challenging with additional weight. Some individuals may be able to articulate both through the hips and through the lower back (i.e. lumbar spine), in which case Erector Spinae also becomes synergist.