Possibly one of the largest pieces of misinformed advice in regards to a golf swing is that the head should remain still. Watch any of the best players in the world closely and you will appreciate that they have an amount of head movement and for some it is a significant amount of head movement. For example if you watch Tiger Woods in full flow you wonder what all of this "keep your head still" advice is all about.
Often the head movement is caused by a chain reaction of events lower down in the body movement, for example, a dipping head in the downswing is often caused by a squatting action of the legs. Some golfers are able to create an extra amount of power and good ball striking consistency by making a significant squatting action with both knees during the transitional phase of a golf swing at the start of the downswing.
From the top of the backswing, the club changes direction by being pulled down behind the body. If a golfer also incorporates a slight squatting action in this phase of the swing, they will find that there is more power to be called upon through the impact phase from the legs and the hips turning aggressively into the impact area. To understand this feeling, try to make some golf swings with locked out straight legs. You will immediately appreciate it is not very powerful and not very dynamic at all. You will lose distance and often lose the ability to strike the golf ball from this position.
A squatting action in the downswing is the reverse of this position. It can create a more dynamic more powerful and a better ball striking impact position. Be conscious that you don't dip your entire body and lose your spine angle into the golf ball as this will result in fat golf shots.