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Euler Angles vs Tait-Bryan angles..?

So in my study of using Euler Angles to represent rotations in euclidean space I came across the following quote that you can find all over the place:

"To add to the confusion, flight and aerospace engineers, when using yaw, pitch, roll (also called heading, attitude, bank) to refer to rotations about the x, y, z axes, respectively, often call these the Euler angles. These x-''y''-''z'' angles are properly known as the Tait-Bryan angles,.."

Wikipedia on Euler angles: "Euler angles are the classical way of representing rotations in 3-dimensional Euclidean space, named after Leonhard Euler."

Wikipedia on Tait-Bryan angles: "In geometry, Tait-Bryan angles are three angles used to describe a general rotation in three-dimensional Euclidean space by three successive rotations, once about the x-axis, once about the y-axis, and once about the z-axis."

So can someone knowlegable in the subject please explain the difference to me? Is it the abstraction? Is this a case of semantics or am I just a large ape that needs to stick to beating a stick?


[Edited:]

Ok, so my understanding is that the difference is this - after each rotation using Tait-Bryan the axis will be redefined, the coordinate system relying on the object itself. Whereas when applying Euler angles the axis will not move. In other words the object defines the coordinate system.







Comments

 

André said:

There are 2 different ways to describe rotations within 3-dim euklidian Space, known also as alpha-beta-alpha or alpha-beta-gamma sequence.

The first one sequentially rotates about the 1st axis of the original system, resulting in an intermediate 2nd system, about the 2nd axis of the 2nd system, resulting in an intermediate 3rd system, about the 3rd axis of the 3rd system, resulting in the final system. The angles used in this sequence are called Tait-Bryan angles (in Europe usally Cardan angles).

The second one sequentally rotates about the 3rd axis of the original system, resulting in an intermediate 2nd system, about the 1st axis of the 2nd system, resulting in an intermediate 3rd system, about the 3rd axis of the 3rd system, resulting in the final system. The angles used in this sequence are called Euler angles.

The usage depends on your application. Usally the inverse transformation is required also. Due to the different sequence, the singularities of the transformations are different. E.g. the Tait-Bryan angles are used in aerospace up to a longitude of 89 degree, but near the poles one has to change to a different set of parameters.

December 7, 2007 2:00 AM

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