Why does the Dzhanibekov effect occur in rotating tennis rackets?

[observer1]

Hello all,

I can understand the mathematics of this phenomena

1. First, one can solve the Euler equations of motion numerically, using Runge-Kutta and plot the motion.
2. Also, the path of the angular velocity vector will like on the kinetic energy ellipsoid and the angular momentum vector.
3. Finally, while angular momentum in the inertial frame is conserved, it does not mean that that components must be constant.

I can ACCEPT (operative word here) all of this and understand the corresponding mathematics (polhodes, etc.)

However, I cannot INTUIT why this effect SHOULD happen: I cannot ANTICIPATE it.

In many cases of physcs, say the Coriolis Effect, I can reason my way through it and justify it.

But could someone explain in WORDS, why this Tennis Racket behavior is expected when an object rotates about the axis that correspeonds to the intermediate moment of inertia?

Or are there some behaviors in he physical world that cannot be SIMPLY explained?

 

[Simon Bridge]

It isn't expected in the common-sense way: it is counter intuitive. Happens a lot in physics: you just get used to it the same way you develop your common-sense intuition like with anything.

 

[wrobel]

For example the Kapitza's pendulum. Another funny thing I just remember is as follows. Imagine very wide horizontal table which rotates about a vertical axis with constant angular velocity. Then you put a billiard ball on this table. You can even provide this ball with initial velocity and rotation. Assume that the ball rolls without slipping. Then the center of the ball describes a circle relative to the stationary observer

 

[observer1]

It isn't expected in the common-sense way: it is counter intuitive. Happens a lot in physics: you just get used to it the same way you develop your common-sense intuition like with anything.

Simon, could you elaborate (that seems silly, huh? elaborate on a simple statement... but here goes)

Can one categorize certain problems as those which are intuitive and those not intuitive? What does it mean to be intuitive?

For example, with centripetal acceleration and centrifugal force, I can "anthropomorphize" the issue and say "you want to keep going forward. But if the frame (say a car turning left) is not inertial, then, it will "push" you to the left. And this give rise to the "conception" of an centrifugal force...

Now in the case of this phenomena, if one does NOT induce a slight perturbation in the OTHER TWO angular velocities, and one assumes a PERFECT DIAGONAL mass moment of inertia matrix, then the phenomena cannot happen mathematically.

Can this be the issue? One cannot "intuit" a case that is not mathematically perfect?

I don't know what I am writing.

But I cannot accept that this cannot be "anticipated."

 

[wrobel]

one assumes a PERFECT DIAGONAL mass moment of inertia matrix

for all rigid bodies the matrix of moment of inertia is perfectly diagonal in the corresponding Cartesian frame. The effect from the movie illustrates the following fact: rotation of rigid body about its middle principle axis is unstable

 

[nasu]

Our "intuition" and ability to predict is based on a set of experiences we had so far. As anybody's experience is limited it would be unreasonable to expect that this intuition will apply to anything you can ever see or encounter. If it look weird or non-intuitive it just means that is something new which you did not encounter before and significantly different from the situations and systems your intuition is based on.
I think this is what Simon's post implied too.

The experience obtained in law school won't make the process of brain surgery very "intuitive" even though everything that happens in a court of law looks very predictable and normal.

 

[observer1]

If it look weird or non-intuitive it just means that is something new which you did not encounter before and significantly different from the situations and systems your intuition is based on.

I can accept this. Say for example, I know nothing about rotations. Then I cannot intuit a centrifugal force.
Also, say that I live on a non-rotating plane. I cannot intuit the coriolis

But once I work out the math and "imagine" such a life, I can immediately intuit both of those effects.

I agree with you (and forgive me: I am not trying to be combative here) but are you suggesting that there is a possible realm of experience where the Tennis Racket flip can be anticipated?

Because nothing you wrote precludes that and then I want to know why.

Where is the statement that ASSURES me that this effect cannot EVER be intuitive?

Is there something in the math itself that assures this?

 

[nasu]

Well, if you had seen this thing happening for many different objects, for a long time, you will probably find it "obvious".
Someone without the experience of gravity will find the fact that an object starts moving by itself when released at some height like something magical, don't you think?
However we don't even think about it when we see it happening. It looks obvious and "intuitive". If I drop something from the roof, I have a good "intuition" about what will happen. But this does not mean I understand gravity in any deep sense. Actually gravity is more "mysterious" than the rotation. If anything, the math and the theory may give a better sense of "understanding" rather than the "intuition" developed by experience.

If you were spending your life throwing objects with low symmetry you will expect what they will do. Maybe even develop some skills about taking advantage of this, when you play with a ball that changes is spinning axis in the air. Too bad the socker balls are so close to a sphere. :)

 

[observer1]

Well, if you had seen this thing happening for many different objects, for a long time, you will probably find it "obvious".
Someone without the experience of gravity will find the fact that an object starts moving by itself when released at some height like something magical, don't you think?
However we don't even think about it when we see it happening. It looks obvious and "intuitive". If I drop something from the roof, I have a good "intuition" about what will happen. But this does not mean I understand gravity in any deep sense. Actually gravity is more "mysterious" than the rotation. If anything, the math and the theory may give a better sense of "understanding" rather than the "intuition" developed by experience.

If you were spending your life throwing objects with low symmetry you will expect what they will do. Maybe even develop some skills about taking advantage of this, when you play with a ball that changes is spinning axis in the air. Too bad the socker balls are so close to a sphere. :)

I sort of agree with your comment on throwing such object often. But that I call "familiarity"

With regard to the Magnus effect: I can explain that in words and pictures by drawing streamlines that separate and sketching out, in words and pictures the pressure drop when fluid flows fast.

But I cannot begin to even imagine a world of repeated experience where I can sketch out this tennis effect.

However, your words on gravity do ring true. So maybe there is somethign there. WROBEL mentioned Kapitza's pendulum. And that involves gravity. Perhaps there is some sort of category there.

Oh I don't know. Maybe I should just accept this and get over it.

 

[A.T.]

Where is the statement that ASSURES me that this effect cannot EVER be intuitive?

Is there something in the math itself that assures this?

Can you define "intuitive" mathematically?

 

[rcgldr]

In the case of a tennis racket, flipping it with the plane of the face (strings) perpendicular to the axis of rotation will work as expected. Flipping it with the the face parallel to the axis of rotation will almost always result in the racket twisting. Sometimes you will be able to get a single flip without it twisting, so the situation is similar to an unstable one. If I recall correctly, you usually get 1/2 twist for each rotation of a flipped tennis racket.

 

[marcusl]

Can one categorize certain problems as those which are intuitive and those not intuitive?

Any phenomena that involve the mathematical curl operator tends to confuse people. Examples include the gyroscopic effect and precession, the Coriolis force, and magnetism. They are counterintuitive perhaps because the source, applied influence and effect (I'm thinking gyroscope here) all act in different directions.

 

[rcgldr]

What's going on with the tennis racket is an imbalance of centripetal acceleration on the sides of the racket head, which produces an internal torque resulting in the racket twisting. Angular momentum is conserved (ignoring effects related to aerodynamic drag).