Any exercise that requires an overhead component is largely considered a core exercise. To improve stability in your overhead movements like Snatch and Jerks, we can apply unstable components to specific movement patterns in order to increase our kinesthetic awareness. One method in particular that I have found to be a huge help over the years are perturbations.
Perturbations are any external disruption of motion or equilibrium. The use of perturbations during overhead activity will require proximal stability. This type of stimulus has great transference into our overhead stability through neuromuscular facilitation of the shoulder and core (abdominals and small stabilizer muscles in the torso). If done correctly, we are forcing intrinsic structures to fire and combat external forces through anti-movement corrections while simultaneously moving through a specific range of motion, in this case range of motion that is specific to overhead patterns present in the Snatch and Jerk.
Below are three exercises that are my favorite 'go-to' perturbations when I am feeling a little wonky overhead. It is important to note that during each of the following exercises, the emphasis should be to avoid any movement of the trunk or torso while completing controlled, full range of motion. Your core should be engaged throughout the entire range of motion, from start to finish.
These exercises do not have to be heavy to be challenging, but can certainly be loaded to add a strength component. As you master the movement, increase instability by using a longer band or by increasing sway of the plates. Remember, CONTROL is everything.