Posted by: JJA () on Sun May 30 12:59:18 2004

Good question.
>
> From the double pendulum demo,we know that when the first pendulum(torso) starts to
> turn,there will ordinarily be some narrowing of the hinge angle with the second
> pendulum(bat) which is the opposite of the way Sheff. turns the bat.Must be some other
> force. ?Dark energy?

Sir,

The point of the double pendulum example is to show that one can generate significant angular velocity of the second link (bat) without applying torque to the second link (bat). It appears that everyone now accepts that premise, which by the way is absolutely correct. Torque on the second link is not required to generate bat speed for a double pendulum system.

The question you are now raising is an excellent one. Is the double pendulum an accurate representation of a human being swinging a baseball bat? Of course, the double pendulum is a gross approximation to such a complicated biomechanical action. It is just two dimensional after all! Why it is useful is that it is mathematically tractable, i.e., simple enough to make computer simulations that can be viewed. That's why Nyman's computer visulation of this action I believe is very useful. Of course, one could, with enough money, make a much more complicated robotic system that would much more closely replicate the human swing. From these simulations one could answer the questions you raise much more easily. Despite what anyone says, what is happening isn't easy to explain or understand.

So let me try to answer your question. I would prefer that someone actually get a video of Sheffields swing and tell me the exact frame and action that you are referring to. The start of the swing for most professionals is actually very complicated. Since Jack does not have a precise definition of top hand torque, and since by Enloe's and my previous discussion one can see that precise definitions are required to understand what is going on, I really think we need a precise video frame to discuss this.

I'll try to answer your question actually based on Jack's video of John Elliot. When he first discusses top hand torque, he has an overhead shot of Coach Elliot. During that video sequence, Coach Elliot actually rotates the bat about an axis approximately through his lead arm. In other words, his bat angle starts out at say 60 degrees from the local vertical, and then rotates down to say 45 degrees from the local vertical. (I'm not viewing the video right now, so these approximate angles are only from my memory. I apologize if I have them wrong.)

There is no question that this is torque being applied to the bat. Call it top hand torque if you like.

The problem is that the torque is being applied in a direction that is not sustainable. Since angular velocity has been generated about that lead arm axis, if this angular velocity does not get zeroed, eventually the bat head will hit the ground! To zero out that angular velocity initially generated by the "top hand torque" requires counteracting torque later in the swing to stop the bat from hitting the ground. Thus, any "early bat speed" generated will be zeroed out later in the swing.

The bottom line is that "bottom hand torque" can very well be applied in some swings. But the description in Jack's video has the torque in a direction that does not contribute to swing speed. So, no, there is no dark energy present in swings. Only forces and moments. But one must think very, very carefully about the directions of the moments and forces in the swing to determine whether they contribute to swing speed or not.

Sorry for the long explanation, but you're getting into physics again.

-JJA

P.S. I will be happy to respond to anyone's questions, but until Jack apologizes to me for his personal attacks, I will not answer his questions. I have never, and will never, ever attack anyone personally on this board. This is a scientific discussion, and Jack can be free to disagree with me. But to question my motives and background on something as extraordinarily difficult from a physics/math perspective is something that I think is unfair and biased, and I won't tolerate it. I would like to think my background can be helpful to some readers, but it's Jack's web site. It's up to him.