OOF2: The Manual

`XYZ (XYZ)`
	6.5.2. Subclasses

Name

XYZ (XYZ) — The "aerodynamic" XYZ convention for specifying an orientation. Rotation by phi about x, then theta about y, then psi about z, brings the crystal axes into coincidence with the lab axes.

Synopsis

XYZ(phi,theta,psi)

Details

Base class: Orientation
Parameters:

phi

Initial rotation about x axis, in degrees. Type: A real number in the range [-180, 180].

theta

Second rotation, about y axis, in degrees. Type: A real number in the range [0, 180].

psi

Third rotation, about z axis, in degrees. Type: A real number in the range [-180, 180].

Description

An XYZ object represents the orientation of a three dimensional object, assumed to be a crystal, in three dimensional space in terms of Euler angles conventionally denoted $\phi$ , $\theta$ , and $\psi$ . In the XYZ convention, as implied by the name, these represent rotations successively about each axis. Similarly to the Abg Euler angles, these define rotations which take the crystal basis vectors $\hat{\mathrm{\bf a}}$ , $\hat{\mathrm{\bf b}}$ , and $\hat{\mathrm{\bf c}}$ into coincidence with the lab (or screen) basis vectors $\hat{\mathrm{\bf x}}$ , $\hat{\mathrm{\bf y}}$ , and $\hat{\mathrm{\bf z}}$ , respectively. The first rotation, associated with $\phi$ , is about the initial crystalline $\hat{\mathrm{\bf a}}$ axis, the second by $\theta$ about the rotated crystalline $\hat{\mathrm{\bf b}}$ axis, and the third by $\psi$ about the doubly-rotated crystalline $\hat{\mathrm{\bf c}}$ axis.

This rotation scheme is one member of a family of rotation schemes, all of which differ only in the order in which the rotation axes are specified for the successive rotations associated with the Euler angles. The XYZ convention is used in the aerodynamics community, where the angles correspond to the pitch, roll, and yaw of a vehicle. In other conventions, such as X, when $\theta$ is small, then $\phi$ and $\psi$ have similar effects, which can be numerically inconvenient. This convention avoids this feature. The nomenclature comes from the second edition of "Classical Mechanics" by H. Goldstein.


`XOver (XOverErrorScaling)`		`Xor (XorSubProblem)`