Euler vs. Tait (steady precession vs... what?)

[Trying2Learn]

TL;DR Summary

what is the analogue of steady precession when using the Tait -Bryan angles

Good Morning

When one studies body rotations, there are two general approaches one uses: Euler Angles vs. Tait-Bryan Angles.

The significant difference is that:

• Tait–Bryan angles represent rotations about three distinct axes (e.g. x-y-z, or x-y′-z″): Yaw, Pitch, Roll
• Euler angles use the same axis for both the first and third elemental rotations (e.g., z-x-z, or z-x′-z″): Precession, Nutation, Spin

With Euler angles, there is a special case of STEADY PRECESSION: precession rate is constant, nutation rate is 0, spin rate is constant.

Is there a NAME for the analogous case, when modeling with Tait? Yaw rate is constant, pitch rate is 0, roll rate is constant?

 

[WHT]

Yes, there is a name for the analogous case in Tait-Bryan angles. It's called "Steady Turn," also known as "Constant Turn" or "Banked Turn." In this case, the yaw rate is constant, the pitch rate is zero, and the roll rate is constant. The term "banked turn" refers to the fact that the vehicle or object is banked or tilted to one side, like an airplane during a turn. This term is commonly used in aviation and aerospace engineering.