This would be a great study for a university physics or eng/phys dept looking for a project - since they'll have the equipment needed to capture the event.
Most engineering departments focus on funded projects, and bringing a firearm to Campus is strictly forbidden almost universally. You'd probably need a seven figure grant to get some exemption from that rule, and I still would not bet on it.
It would be easier for the project to be done off campus at an existing range, but then you have the challenge of getting the needed equipment to capture the event to the range. The systems are not usually designed for portability. It can be done though, but who is paying for it?
Finally, using high speed tri-axial accelerometers attached to the barrel can quantify its motion much more accurately than most high speed videos available in mechanical engineering departments. Casual shooters may prefer to "see" what is happening in a video, but mechanical engineers have greater appreciation for accurate graphs of barrel acceleration, velocity, and position vs. time. The instrumentation here is much less expensive also, and in many cases easier to get to a range.
You might try a search for something like high speed acceleration measurements of rifle barrels.