Understanding the Differences between Euler Versus Tait Angles

[Trying2Learn]

TL;DR Summary

Which to use; and in which problems: Tait or Euler angles?

Good Morning!

I understand that the definitions and notations used for Tait–Bryan angles are similar to those described above for proper Euler angles, and I can work problems in either. However, I lack the ability to "rise above both" and categorize them.

I do understand that the only difference is that Tait–Bryan angles represent rotations about three distinct axes (yaw, pitch, roll) , while Euler angles use the same axis for both the first and third elemental rotations (precession, nutation spin).

That said, it SEEMS to me that Euler angles are preferred in mechanical engineering
Tait are preferred in marine and aerospace

Is there any reason (or any special problems) such that one is better than the other? Or does it really not matter?

And while I am at it: why do we talk about "steady PRECESSION" and never "steady YAW"

 

[jedishrfu]

Here's a video description of the various rotations, although watching it may give you vertigo.

https://www.google.com/search?q=pro...#fpstate=ive&vld=cid:f140b514,vid:wV59Xg-sm70

and here's a cheat sheet comparison of the types of rotations:

http://www.clinicalgaitanalysis.com/faq/angles.html

I did see some references that said Tait-Bryant angles were more suited to particle motion. It seemed the Euler angles suffer from gimbal lock in certain rotation combos, losing one degree of freedom, whereas Tait-Bryant angles don't have this issue.

https://en.wikipedia.org/wiki/Gimbal_lock

Vaguely I recall using Frenet-Serret formulas to set up a coordinate system relative to the particle traveling along a trajectory using a tangent vector, normal vector, and their cross-product to define axes relative to the object.

https://en.wikipedia.org/wiki/Frenet–Serret_formulas

Perhaps @Mark44 or @fresh_42 can explain this better.

 

[FactChecker]

It seemed the Euler angles suffer from gimbal lock in certain rotation combos, losing one degree of freedom, whereas Tait-Bryant angles don't have this issue.

https://en.wikipedia.org/wiki/Gimbal_lock

I think that Tait-Bryant still has gimbal lock problems. Your first linked reference indicates a gimble lock problem.

and here's a cheat sheet comparison of the types of rotations:

http://www.clinicalgaitanalysis.com/faq/angles.html

IMO, if the gimble lock problem could be avoided by using Tait-Bryant instead of quaternions, then quaternions would not be used nearly as much.