rotation2quat

Given a rotation matrix \(C^{AB}\) rotating the frame A onto B, the function returns the minimal “positive angle” quaternion representing this rotation, where the quaternion, \(\vec{\chi}\) is defined as:

\[\vec{\chi}= \left[\cos\left(\frac{\psi}{2}\right),\, \sin\left(\frac{\psi}{2}\right)\mathbf{\hat{n}}\right]\]

param Cab:

rotation matrix \(C^{AB}\) from frame A to B

type Cab:

np.array

returns:

equivalent quaternion \(\vec{\chi}\)

rtype:

np.array

Notes

This is the inverse of algebra.quat2rotation for Cartesian rotation vectors associated to rotations in the range \([-\pi,\pi]\), i.e.:

fv == algebra.rotation2crv(algebra.crv2rotation(fv))

where fv represents the Cartesian Rotation Vector, \(\vec{\psi}\) defined as:

\[\vec{\psi} = \psi\,\mathbf{\hat{n}}\]

such that \(\mathbf{\hat{n}}\) is a unit vector and the scalar \(\psi\) is in the range \([-\pi,\,\pi]\).