Book to understand Euler angles (and Tait–Bryan )

In summary, Euler angles and Tait-Bryan angles are two methods for representing the orientation of an object in three-dimensional space. They are important in fields such as aerospace engineering, robotics, and computer graphics, as they provide a convenient and intuitive way to describe an object's orientation. The main difference between the two lies in the order of rotations, and they can be calculated using different methods depending on the application. Common applications include flight dynamics, robotics, computer graphics, and virtual reality.
  • #1
Avatrin
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Hi

I am trying to understand Euler angles and why they work. What are some great books to use as a resource to build a deeper understanding of them? I want to know why 3-2-1 Euler angles are so commonly used, and proofs regarding the mathematical properties of this method..
 
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  • #2
Euler angles are simply a way of parametrizing an arbitrary rotation from one frame to a rotated frame. Have you tried the Wikipedia article below? It is a good starting place.

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

1. What are Euler angles and Tait-Bryan angles?

Euler angles and Tait-Bryan angles are two different methods for representing the orientation of an object in three-dimensional space. They both use a set of three angles to describe the rotation of an object around its three axes.

2. How are Euler angles and Tait-Bryan angles calculated?

Euler angles are calculated by sequentially rotating an object around three axes: first around the z-axis, then the new y-axis, and finally the new x-axis. Tait-Bryan angles, on the other hand, are calculated by rotating an object around the initial axes, then around the intermediate axes, and finally around the final axes.

3. What is the difference between Euler angles and Tait-Bryan angles?

The main difference between Euler angles and Tait-Bryan angles lies in the order of rotations. In Euler angles, the rotations are always performed around the fixed axes of the object, while in Tait-Bryan angles, the axes change with each rotation.

4. What are the advantages of using Euler angles and Tait-Bryan angles?

Euler angles and Tait-Bryan angles are commonly used in computer graphics and robotics because they provide a simple and intuitive way to describe the orientation of an object. They also allow for easy decomposition of complex rotations into simpler ones.

5. What are some common applications of Euler angles and Tait-Bryan angles?

Euler angles and Tait-Bryan angles have a wide range of applications in fields such as aerospace engineering, virtual reality, and motion capture. They are also commonly used in video games and animation to control the movement of characters and objects.

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