This is not meant to be in any way an analysis of any of the accidents mentioned in the above posts, but will hopefully help explain what they're referring to as mast bumping.
Mast bumping is generally accepted as being caused by incorrect lateral cyclic inputs when the aircraft is in a 'negative g' situation.
'Negative g' can be caused by either turbulence, or induced by the pilot by 'bunting' the helicopter over as brads correctly explained.
If the 'negative g' unloading is sufficient enough, the thrust vector from the tail rotor can cause the fuselage to roll while the disk is in an unladen state.
The correct action is to first gently apply aft cyclic to regain the disk loading (to make the fuselages weight hang from the blades again) before any lateral (sideways) input can safely be made.
However, if lateral cyclic is used first to counteract this apparent uncommanded roll, the blades can flap excessively and possibly contact the mast with the inner head assembly at the blade root end.
Two bladed teetering systems are particularly susceptible to this phenomenon and pilots are trained to understand, identify and correct this phenomenon associated with 'negative g' situations.
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