An important current in golf teaches that one should let the club do its thing and interfere the least possible. Usually one refers to centrifugal force as the main element in such instruction.

One well known golfer/author using this approach is George Knudson. Rather contrasting to HK’s he shies away from details and reduces the swing to a few very simple basic elements.

Knudson’s paradoxical advice is to ‘give up control to gain control’. Let’s see with a simple double pendulum math model if this holds any water.

The upper segment of the pendulum is modeled as two equal 0.3 m length segments, with respective masses of 4.2 and 2.4 kg.

The hands are modeled to be integral part of the golf club and modeled as a 1 kg point mass. Shaft length 1.2 m with mass 0.07 kg and clubhead as a 0.2 kg point mass.

There will be two linked pages and we start with the first one [size=125]here[/size] where we look at the effect of arm/club angle.

It is indeed interesting to see a rather strong self regulating mechanism at work and without which a golf swing would likely be not quite feasible. :sunglasses:

George clearly ripped it left in his prime playing years… then later focused on a teaching career. I can only assume that he may have taught more of a swingers move to the average golfer figuring few would work as hard as he did to become a fine hitter.

His Bermuda video was certainly more relaxed looking going through impact than 15 years earlier, but it was far from a full on TGM style dump it out to right field move.

One might suggest a relaxing walk on the beach, but to do so, the legs are hardly relaxed, especially walking in sand.
We get used to a certain level of muscular tension, and any amount less than that could be perceived as a relaxed state.

To me George was absolutely viscous going through impact in his prime. A more relaxed version of that “to him” may have given the sensation of dead hands, and now conscious involvement, but I still think in Bermuda, he was pulling very hard against CF post impact. His torso wasn’t accelerating post impact to the degree it did in the 1960’s but it still was VERY good.


The aim of my post was to draw attention to the apparent servo control type of mechanism active in golf swing.

I should perhaps not have mentioned George Knudson, or anyone else, for that matter.

Let’s think simply of an Iron Byron, swinging a club, that will center the discussion back on Mother Nature giving golfers a helping hand. :wink:

How you derive the pedula angles in those pictures; from real data; mathematical progression or something else.

I think it would be interesting to see the difference between whether or not the left arm and shaft are allowed to move passively inline (from a DTL view) or if the angle of the shaft and left arm are preserved from P3 to P4, held firm by resisting forces applied through hand strength.

In your diagram it appears this would support cupping the left wrist at the top of the swing which would increase the angle.

thanks for posting.


The great fun with math models is that it allows to find readily answers for questions which you can’t really ask a real golfer or sometimes even a robot golfer.

For instance how come the club always seems to release the same way at the bottom without me giving it any thought?

So you fancy some approach with the model to find out a bit more about this question.

So I chose three different angles at the top, not necessarily realistic for a real golfer, and applied the same constant torque at the inner pivot.

A dead stop is modeled (green), wrists are thus chosen to be passive and hence only an inertial torque is acting on the ‘wrists’ joint.

The results is indeed quite conclusive - the inertial torque generated seems to ‘adjust’ itself automatically to have the club release almost the same way, largely independent of tinitial angle.

Considering all this does not help you to improve your swing but it is fun and rather satisfying to know this mechanism, i.e., for the curious mind. :wink:


Presently the calculations were done for passive wrists. But what you are looking for as comparison requires a rather more sophisticated 3D model to include roll of arms. Flailing acts as a velocity multiplier. Holding the arm/club angle for as long as possible maximizes this action and assures a clean hit. Also at some point in the downswing the club has to release to make contact with the ball. :wink:

Do you suppose this is why Homer completely ignored it in TGM? Possibly he couldn’t really wrap his head around it? even though it was used by many of the games finest strikers?

I agree that it does become more of a 3D imaging concept, and TGM seems mostly explained in 2D diagrams.

I think it is much easier to experience from the cockpit, than map it all out. I suppose Homer not being a great player, or certainly not having a swing that cut it left, held wristcock and fired with active hands, with a post impact accelerating pivot… left him not able to properly catalog it.


We, humans, like to generate concepts. However once established they often take on a life for themselves. They first are enlightening but subsequently they frequently act as a hindrance for further free thinking.

Isaac Newton’s great popularity, a real genius, also became a hindrance, not generally known. After his death, any new idea to be accepted by the Anglo Saxon scientific community as truly scientific had to have an equivalence using springs and masses. This clearly did not make it easy with the rather abstract new scientific ideas emerging, especially in continental Europe.

Hence more an idea/concept is heralded more one should be aware of its potential negative side effect. Such is the case for the concepts such as circle and plane, at the heart of TGM thinking. It first appears indeed to be very attractive but once self appointed ‘gurus’ take hold of it, it rapidly becomes a rigid type of religious affair, preventing to truly think golf in 3D as should be the case.

[size=125]Second part of bio-servo-control[/size] where we look at the the impact conditions when the starting angle is kept constant and instead the central torque is varied.

Hello mandrin,

Does the location of low point change if the starting angle is kept constant and the central torque is varied?

Thank you.

Hello mandrin,

Does the location of low point change if the starting angle varies and the central torque is kept constant?

Thank you,


I have arbitrarily chosen the ball position to be opposite the central pivot. If you look at Figs 1, 2, 3 in the two linked posts you will notice that the behavior of the club up to and at impact is either very similar indeed or looking identical. One can therefore deduce, even if it is not specifically indicated, that the low point is indeed very similar for the various cases. However I will in a few days do a more precise analysis.