Overdoing it on the golf swing model

2016 April 21
by Daniel Lakeland

So, pretty much everyone has analyzed the golf swing as a rigid double pendulum. Since that's well understood (see "The Physics of Golf" for example), the question I have is what is missing from this analysis? The way to answer that is to make a slightly more complex model that potentially captures different effects, and see if any of them are worth considering.

The model I'm considering has a spine pivot that can translate left-right, a rigid left arm, a variable length, actuated, right arm, two hand attachment points separated by a small distance at the grip, and a club with two stiff torsional spring joints in the shaft, to capture some shaft bend. Furthermore, you could add the golf ball itself with a very stiff nonlinear spring whose interaction force goes to zero rapidly outside the radius of the ball but goes to infinity rapidly as the club approaches the center of the ball.

The problem with this model is that it is a nonlinear actuated control system. What you'd like to do is specify the spine torque, the weight shift, the wrist torques, and the right arm extension as parameterized functions of time or of angle, and then train the system to maximize the component of ball velocity along the target line subject to constraints on the available torque, forces, etc. Then once it's found it's "perfect swing" you'd want to figure out what it's doing by looking at the chosen input functions.

Not exactly a trivial code it up at home in an afternoon kind of problem, but an interesting area of research. I'd be particularly interested in whether the shaft flexibility really has much effect. After all, the fancy expensive golf clubs are often expensive and fancy because they have graphite shafts and soforth. The bend of the shaft is visible in all the high speed videos as well.

 

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