A Euler, Tait-Bryan, Tait, proper, Improper

  • A
  • Thread starter Thread starter Trying2Learn
  • Start date Start date
  • Tags Tags
    Euler
AI Thread Summary
The discussion revolves around the confusion surrounding the naming conventions of rotation angles, specifically Euler and Tait-Bryan angles. There are 12 possible rotations classified as Euler angles, with distinctions made based on whether the third axis is repeated. Proper and improper rotations are defined by whether they occur about internal or external axes, leading to four classifications: improper Euler, proper Euler, improper Tait-Bryan, and proper Tait-Bryan. The conversation highlights the inconsistency in terminology across different sources and the importance of understanding the definitions used in describing these rotations. Additionally, it notes that Tait-Bryan angles are often associated with aircraft movements (pitch, yaw, roll), while the conventions for ships remain unclear.
Trying2Learn
Messages
375
Reaction score
57
TL;DR Summary
Euler, Tait-Bryan, Tait, proper, Improper: total confusion
Can I try again?

I have seen (on the web), all these names, DISTINCTLY: Euler, Tait-Bryan, Tait, proper, Improper

I am still trying to make sense of this and am facing some strange naming conventions. I now can see this (the actual math does not concern me--it is only the names that cause me confusion):

There are 12 possible rotations

121 131 212 232 313 323
123 132 213 231 312 321

All are called Euler angles (which is odd to me)

If the third axis is NOT repeated (red ones, above): they are called Tait-Bryan angles
If third one is repeated, they are called Euler angles (YES; USING THE SAME NAME--should this have been called Euler ROTATION PROCESS to distinguish from Euler Angles)

Then there are proper/intrinsic vs improper/extrinsic:

When the rotations are improper/ EXtrinsic: it means they happen about fixed spatial axes (the axes are EXternal to the body)

When the rotations are proper/INtrinsic: it means they happen about fixed spatial axes (the axes are INternal to the body--attached to it)

This suggests FOUR cases:
  1. Improper Euler
  2. Proper Euler
  3. Improper Tait-Bryan
  4. Proper Tait-Bryan

Sometimes, I read about Tait angles (without any mention of Bryan) and some seem to call them Euler, but I assume they are referencing the very nature of angles (12 sets) and not the distinction on whether an axis is repeated. I think.

Can someone comment on this?
I cannot quote a source but so many websites do this.
It seems to me that Wikipedia gets it right: https://en.wikipedia.org/wiki/Euler_angles
But they fail to address other possibilities
And they fail to explain how and why each is used (limits, advantages)

Do I have it correctly?

Finally, with planes, we talk about Tait-Bryan, but with a condition: 1-faces forward, 2-to the right and 3-down In other words, these angles are mapped to how planes fly, and the names, in order of the sentence just above this one, is: pitch, yaw, roll

What is the convention with ships?

My head his spinning. ChatGPT, I think, makes this even worse and gets it all wrong.

I now also think that one cannot discuss steady precession when an axis is repeated: it only happens in the BLUE set, above.
In other words, there is no corresponding notion of steady precession with Tait-Bryan because all axes are different.
 
Last edited:
Physics news on Phys.org
Naming conventions are just, well, conventions and may depend on the author using them. One just has to make sure to check the definition of the angles used to describe rotations.
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
Thread 'Recovering Hamilton's Equations from Poisson brackets'
The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing. The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##. But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
Back
Top