# Understanding the Differences between Euler Versus Tait Angles

• Trying2Learn
In summary, the Euler angles suffer from gimbal lock in certain rotation combos, whereas Tait-Bryan angles do not.
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"

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

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.

Last edited:
jedishrfu said:
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.
jedishrfu said:
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.

## What are Euler angles and Tait angles?

Euler angles and Tait angles are two different systems used to represent the orientation of a rigid body in three-dimensional space. They both use a set of three angles to describe the rotation of the body around three axes.

## What is the difference between Euler angles and Tait angles?

The main difference between Euler angles and Tait angles is the order in which the rotations are applied. In Euler angles, the rotations are applied in a specific order, while in Tait angles, the rotations can be applied in any order as long as they are around different axes.

## Which one is more commonly used in science and engineering?

Euler angles are more commonly used in science and engineering because they are easier to understand and visualize. They are also more intuitive when working with objects that have a fixed orientation, such as aircraft or spacecraft.

## What are the advantages of using Tait angles over Euler angles?

The main advantage of using Tait angles is that they are more mathematically elegant and can be used to describe any rotation in three-dimensional space, whereas Euler angles are limited to specific types of rotations. Tait angles are also less prone to the problem of gimbal lock, which can occur with certain orientations in Euler angles.

## Are there any drawbacks to using Tait angles?

One drawback of using Tait angles is that they can be more difficult to understand and visualize compared to Euler angles. Additionally, Tait angles require more calculations and conversions to switch between different coordinate systems, which can be time-consuming and prone to errors.

• Classical Physics
Replies
1
Views
785
• Classical Physics
Replies
1
Views
536
• Classical Physics
Replies
1
Views
734
• Classical Physics
Replies
7
Views
908
• Classical Physics
Replies
7
Views
845
• Classical Physics
Replies
8
Views
1K
• Mechanics
Replies
7
Views
1K
• Linear and Abstract Algebra
Replies
6
Views
1K
• Classical Physics
Replies
6
Views
1K
• Classical Physics
Replies
2
Views
944