Philosophy of Argument
In that the nature of this argument is at best ill defined and subject to the whims of whoever is posting, I'm going to try and define it once again. This will not be much about coaching or physics, but the nature of the discussion at hand.
In Defense of the Petrov Method
I should point out that there has never, never been put forth any sort of idea by me that 1) the Petrov method doesn't work 2) that one shouldn't use it. Why? Because it works. In this, it has established pragmatic value. In fact I have advocated its use. As for one, because as Tim points out, its easier, and then for a variety of reasons safer. It has earned this pragmatic value by the results. A long list of world records, Olympic golds, WC champions and medal earners. It works. In part then when "coaching" comes up in these discussions, it doesn't mean a lot to me for when we are talking about physics we are only very tangentially and tenuously talking about "coaching". As before, one can be a good to great pole vault coach, and know little to nothing about physics.
The Value of Science
Science, the scientific method, and the use of data and math have their own history of pragmatic value. It works. That history is longer and less in doubt than speculation on the methodology of the pole vault.
When one is coaching the vault one need not, and in fact very often needs to avoid the use of scientific nomenclature. Science speaks little of intent. What it does do however is describe and predict the action of physical systems. Thus if you are going to describe how the vault works (and this is NOT coaching it) you are going to have to use physics, the method of the scientific method, and the nomenclature of science. NOT the vault. All of the pragmatic weight of the success of the Petrov method means NOTHING here except that the coaching works as coaching, not at all relevant to having any ability to describe the system. This is why the continual push that in "describing" the system one should use "pole vault" terms is flawed, off base, and purely political as an attempt to square the dialog in a certain camp. No. In fact, quite the opposite is true. IF one wants to work on describing the system scientifically, then one has to use and adhere to the scientific as it has its own pragmatic value in these matters.
So my purpose here has been along this divide. One one side you have the value of the Petrov coaching method, and then from that, from that value there is taken a license to use that value over and above the value science and physics has established. That anything that can be said descriptively is backed up by the performance value. It is not. So there are a long list of problems in this fashion where the "science" put forth is just bad science. Further its put forth that again the performance value finalizes some claims from the PB adherents that it singularly and solely is "scientifically" proven to be the singular best "model" of the vault. This I doubt and that sort of "proof" I have not seen. Not even close. What is often demanded I "prove" is, oddly enough to "prove" that I can have this doubt.
My own knowledge of physics and this system leads to an intuitive guess that it is a problem that has not singular solution but a set of equilibrium points. Or, many solutions. So there would be no "singular model" to find. So it is my exception to such claims. Petrov method? Use it! "Model"? I don't buy it...
Thanks to Tim for bringing his point of view on several of the points I've been working on. With the stiff pole keeping the COM low and on a certain path in time was paramount as the pole did not bend much if at all. The question now arises that since the new pole does bend AND has a compression RATE relative in part to gravity, is this idea more or less important? SO a further question. IF a vaulter can maximize the effect of gravity on compression and thus increase the speed of compression, the rate of energy storage in the pole, the speed of shortening of the chord length, is there not a possible advantage there? Well, the answer is a simple yes with the caveat that the event is full of trade offs.
Whatever might be said of the takeoff, Lavillenie does not swing like the Petrovians. That is visibly evident. Visibly evident that he does not do much of anything to maximize his swing velocity anywhere along the swing. My view is that he keeps the COM under the top hand as much as possible keeping as much gravity compression on the pole as possible. Then, at the point of mid swing when the Petrovians are working to achieve maximum swing velocity he's aggressively pulling himself up UNDER the top hand. There is an action/reaction moment at this time that effects the compression force and thus chord length of the pole, once again keeping it moving forward at a better rate. In as much as you can see the swing force in the pole for Petrovians like Bubka, you can see this "tuck" force for Lavillenie. And so here's the thing. You can't really have it both ways. You cannot have both the high Petrovian swing force and the Lavillenie "tuck" force. Which is better? I've seen nothing mathematical or scientific to prove which is better, but I believe Lavillenie's results keep the question in doubt as to the veracity of making such a claim.
My intuition on the subject now is that the Petrov method benefits longer vaulters more, while shorter vaulters find better results with a differing method. Namely one more aligned with the one he and a list of other great shorter vaulters have steered towards. This has to do with the nature of the vaulters anatomy/structure as a "lever" in the vault. That they are going to suffer diminished results if they cock the left arm and allow the system to "free" swing forward at the shoulder, hinging the shoulder. Being a shorter lever, and generally lighter, they "see" a threshold limit in trying to maximize energy in the whip swing while losing compressive force on the pole that steers them toward something more like Dial, Buckingham, Greg Duplantis. Can I prove this? No. But not any worse than there is any scientific proof for the idea that the Petrov model is singularly maximized.
Here I will note Mondo Duplantis set his last age group (17' 4.5" copying RL).
With plant problems...https://www.youtube.com/watch?v=REQv-p0SHYE
This is notable to me as he can apparently "copy" just about anyone(apparently he can do Huffman's vault). And so IF he is choosing this style perhaps its because he's getting the best results with it. Or, maybe its just what the cool kids are trying at the moment...