It is clear from the explicit form in terms of Euler angles that the map just described is a smooth, and onto group homomorphism.
42.
The Euler angles then describe the transition from the sample s reference frame into the crystallographic reference frame of each individual grain of the polycrystal.
43.
These discontinuities are caused by the existence of many-to-one mappings between the Euler angle parameterization of the set of 3D rotations.
44.
Sets of rotation axes associated with both proper Euler angles and Tait Bryan angles are commonly named using this notation ( see above for details ).
45.
The standard parametrization consists of three Euler angles ( ? 12, ? 23, ? 13 ) and one complex phase ( ? 13 ).
46.
Rotation formalisms in three dimensions # Conversion _ formulae _ between _ formalisms describes how to compute Euler angles of a rotation from the rotation matrix.
47.
These Euler rotations are related to the proper Euler angles, which were thought to study the movement of a rigid body such or a planet.
48.
There are = 27 possible combinations of three basic rotations but only = 12 of them can be used for representing arbitrary 3D rotations as Euler angles.
49.
I could manually input things through Euler angles, but that's such a pain, since I'd need to compute them back manually.
50.
Sets of rotation axes associated with both proper Euler angles and Tait-Bryan angles are commonly named using this notation ( see above for details ).
