HepRotation Class

HepRotations may be expressed in terms of an axis $\hat{u}$ and angle $\delta$ of counter-clockwise rotation, or as a set of three Euler Angles $(\phi, \theta, \psi)$. Definitions and conventions for these classes match those described in § for directly rotating a Hep3Vector:

$$\mbox{HepRotation}(\hat{u},\delta) \Longrightarrow$$

$$\left( \begin{array}{ccc} \cos \delta + (1 - \cos \delta ) u... ..._x & \cos \delta + (1 - \cos \delta ) u_z^2 \end{array}\right)$$ (136)

$$\mbox{HepRotation}(\phi, \theta, \psi) \Longrightarrow$$

$$\left( \begin{array}{ccc} \cos \psi \cos \phi - \sin \psi \c... ...phi & - \sin \theta \cos \phi & \cos \theta \end{array}\right)$$ (137)

The Euler angles definition matches that found in found in Classical Mechanics (Goldstein), page 109. This treats the Euler angles as a sequence of counter-clockwise passive rotations; that is, the vector remains fixed while the coordinate axes are rotated--new vector components are computed in new coordinate frame.

HEP computations ordinarily use the active rotation viewpoint. Therefore, rotations about an axis imply active counter-clockwise rotation in this package.

Consequently, a rotation by angle $\delta$ around the X axis is equivalent to a rotation with Euler angles $(\phi=\psi=0, \mbox{ } \theta = - \delta)$ and a rotation about the Z axis is equivalent to a rotation with Euler angles $(\theta = 0, \mbox{ } \phi=\psi= - \delta/2)$.