Direct vs. Retrograde Precession

[JTC]

(This is not about the motion of the planets.)

If one takes a body in space (not outer space, necessarily) with only central forces, it may exhibit one of two types of precession: direct or retrograde.

If the body is flat, the precession is retrograde: the spin and precession rates have opposite signs (e.g.: a coin)
If the body is elongated, the precession is direct: the spin and precession rates have the same signs. (e.g.: an American football).

My question is: why does this matter? (I understand why it happens).

Mostly, I am concerned with satellites.

For example most satellites are elongated and will exhibit direct precession.

Do they design them with that in mind? Is there an inherent stability to direct precession?

Why do books call this out? If they call it out, they should at least discuss how it impacts the "design" of objects.

(Flying saucers will exhibit retrograde precession, but there are no flying saucers.)

And it does not have to concern satellites. The fact is: it is a phenomena. So, with that, how is it exploited (if at all) in engineering design? Or is it just simply an observation that has no consequence in the real world.

Or this:

• An American football will enter direct precession.
• A Frisbee will enter retrograde precession.

Knowing this, does it alter how it is thrown?

 

[Filip Larsen]

Spin around the symmetry axis of such elongated semi-rigid bodies is unstable (see for instance the loss of Explorer 1) and will, due to dissipation of rotational energy, eventually end with spin around the inertial long axis. Spin of oblate bodies around the symmetry axis is stable. This fact is rather important in satellite design and operation for maintaining rotational control.

 

[JTC]

Spin around the symmetry axis of such elongated semi-rigid bodies is unstable (see for instance the loss of Explorer 1) and will, due to dissipation of rotational energy, eventually end with spin around the inertial long axis. Spin of oblate bodies around the symmetry axis is stable. This fact is rather important in satellite design and operation for maintaining rotational control.

OK, I see that. But now may I ask this: WHY?

Why is it that DIRECT PRECESSION is more unstable? I would have imagined that RETROGRADE precession would be unstable since the precession rates and spin rates are opposite.

 

[Filip Larsen]

OK, I see that. But now may I ask this: WHY?
Why is it that DIRECT PRECESSION is more unstable? I would have imagined that RETROGRADE precession would be unstable since the precession rates and spin rates are opposite.

I would think it is easiest to understand the reason for spin axis stability by regarding the rotational energy (as previously mentioned). Keeping rotational momentum constant it is fairly straight forward to find an expression for rotational energy for spin around the minor and major principal inertial axis of a rigid body and (with some hand waving) argue that rotation with maximum energy is unstable and minimum energy is stable (since a free body can dissipate rotational energy but its momentum is fixed). Understanding the exact mechanics behind this require more details of course, but it is included in many textbooks on mechanics (like Goldstein's "Classical Mechanics").

I doubt that it will make particular good sense to try understand rotational stability as a consequence of whether precession is prograde or retrograde. Perhaps others here can provide some insight whether there is any useful relationship between precession and stability other that they correlate due to a common mechanical cause.

 

[JTC]

I would think it is easiest to understand the reason for spin axis stability by regarding the rotational energy (as previously mentioned). Keeping rotational momentum constant it is fairly straight forward to find an expression for rotational energy for spin around the minor and major principal inertial axis of a rigid body and (with some hand waving) argue that rotation with maximum energy is unstable and minimum energy is stable (since a free body can dissipate rotational energy but its momentum is fixed). Understanding the exact mechanics behind this require more details of course, but it is included in many textbooks on mechanics (like Goldstein's "Classical Mechanics").

I doubt that it will make particular good sense to try understand rotational stability as a consequence of whether precession is prograde or retrograde. Perhaps others here can provide some insight whether there is any useful relationship between precession and stability other that they correlate due to a common mechanical cause.

Perfect response and exactly what I am looking for. Yes, I will now study the stability with regarding to angular momentum and kinetic energy. I see that is the way to go.

But your phrasing in the second paragraph of your response is EXACTLY what I am ALSO looking for.

I hope someone can respond. Thanks for rephrasing it for me!

(Is it possible that in retrograde precession, the reversal of rotations has a "corrective" or "stabilizing" effect -- I don't know what I am saying; I am grasping.)

(Because I really would have expected it to be the other way: that opposite rotations are more unstable. Unless the nature of prograde vs retrograde is not relevant at all, until the object has an excessively LONG nature vs. flat)