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 \([-\pi,\,\pi]\).