I am pretty much a TGM rookie. But until you get better answers you might just as well try my current interpretation (based on reading here and there):
Stationary is not the same as sitting in a vise. The idea is that it should not move all over the place.
The head will swing slightly, but focus on keeping the upper part of the spine stationary (= the tab inside the collar of your shirt) through the swing.
Do not let it bother you too much what the head does after impact. It has to go.
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When James Durham recorded 94 at the Old Course at St Andrews in 1767, he set a course record that lasted 86 years. Golf: A curious sport whose object is to put a very small ball in a very small hole with implements ill desiged for the purpose - Sir Winston Churchill