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Quaternions are hypercomplex numbers used to represent spatial rotations in three dimensions. This set of routines provides a useful basis for working with quaternions in Octave. A tutorial is in the Octave source, scripts/quaternion/quaternion.ps.
These functions were written by A. S. Hodel, Associate Professor, Auburn University.
w = a*i + b*j + c*k + d |
from given data.
q = [w, x, y, z] = w*i + x*j + y*k + z qconj (q) = -w*i -x*j -y*k + z |
Let Q be a quaternion to transform a vector from a fixed frame to a rotating frame. If the rotating frame is rotating about the [x, y, z] axes at angular rates [wx, wy, wz], then the derivative of Q is given by
Q' = qderivmat (omega) * Q |
If the passive convention is used (rotate the frame, not the vector), then
Q' = -qderivmat (omega) * Q |
Let Q be a quaternion to transform a vector from a fixed frame to a rotating frame. If the rotating frame is rotating about the [x, y, z] axes at angular rates [wx, wy, wz], then the derivative of Q is given by
Q' = qderivmat (omega) * Q |
If the passive convention is used (rotate the frame, not the vector), then
Q' = -qderivmat (omega) * Q. |
q = [w, x, y, z] = w*i + x*j + y*k + z qmult (q, qinv (q)) = 1 = [0 0 0 1] |
[w, x, y, z] = w*i + x*j + y*k + z |
identities:
i^2 = j^2 = k^2 = -1 ij = k jk = i ki = j kj = -i ji = -k ik = -j |
v = q*v/q
.
vi = (2*real(q)^2 - 1)*vb + 2*imag(q)*(imag(q)'*vb) + 2*real(q)*cross(imag(q),vb) |
Where imag(q) is a column vector of length 3.
[vv, th] = quaternion (qib)
.
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