Corresponding case of steady precession but for Tait-Bryan angles

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In summary, the conversation discusses the differences between using Euler angles and Tait-Bryan angles for rotational movements in a body frame. While Euler angles have a special case of steady precession, there is no corresponding phenomena in Tait-Bryan angles. This is because the choice of angles depends on the specific problem being modeled, and there is no need to draw a parallel between the two. It is not sensible to ask about a special case for Tait-Bryan angles, as it is not applicable in the same way as it is for Euler angles. This is due to the different applications of each type of angle.
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TL;DR Summary
What is the corresponding case of steady precession but for Tait-Bryan angles
(This has continued to bother me. I tried asking, and no response. May I please try again?)

Using Euler angles, we rotate about an axis (often, axis three of a gyroscope frame), then a second (axis one of the gimbal frame), then return to the same axis as the first one (back to axis 3, but of the rotor frame) (all in the moving body frame): Precession, then Nutation, then Spin.

Using Tait Bryan angles, we go through a simliar process but this time, all three axes are different: Yaw, pitch, roll?

For Euler angles, there emerges a special case of Steady Precession:
1. Precession RATE constant
2. Nutation constant
3. Spin RATE constant

What is the corresponding phenomena for the Tait-Bryan angles?
Or is that a non-sensical question? And why?

Sometimes, I think the case of steady precession is only for mechanical devices, and can best be described using Euler angles (precession, nutation, spin); and that there is NO SUCH corresponding phenomena when modeling a ship or plane using Tait Bryan (pitch, yaw, roll).

I think I am being a bit OCD trying to draw a parallel. I think I should accept the fact that one just choose the most suitable angles for the problem at hand, and just note that there is a special case of steady precssion for Euler angles (gyroscopes) and not for Tait-Bryan (planes and ships)

Thus, is it ridiculous to even ask about a special case when using Tait Angles (as we do with Euler angles)?

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Your understanding is correct, there is no corresponding phenomena for Tait-Bryan angles. This is because Tait-Bryan angles are commonly used to describe the orientation of planes and ships, which do not exhibit the same type of precession as a gyroscope. The concept of steady precession only applies to rotational motion, and planes and ships do not typically experience this type of motion. Therefore, it is not necessary to try and draw a parallel between the two coordinate systems. As you mentioned, the choice of which angles to use depends on the problem at hand, and in this case, Tait-Bryan angles are more suitable for describing the orientation of planes and ships. It is not ridiculous to ask the question, but it is important to understand the limitations and differences between the two coordinate systems.

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