Quaternion Rotation formula - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Quaternion: composition of rotations orientations to determine relative . . . Remember the operations work from right to left, so the right terms represents a vector from the B frame to E frame, then the second one represents a vector from the E frame to the A frame Thus the composition of the to gives you a quaternion from B to A (i e the orientation of frame B in frame A) (I am speaking in the passive picture here )
Quaternions and spatial translations - Mathematics Stack Exchange $\begingroup$ The alternative is the dual quaternion, which Gerard mentioned (albeit not by name) - they are composed the same way, the "sandwich" (a)(bcb*)(a*) = (ab)c(ba) = (ab)c(ab)*, which means a long sequence on the LHS only needs to be conjugated after the fact to find the RHS So, you don't need to break a long sequence of quaternions
Understanding quaternions - Mathematics Stack Exchange Adding two unit quaternions generally does not yield a unit quaternion, so the answer is technically no as written, but the answer is yes if you say "rotating two separate planes by the same angle and rescales " Of course adding two quaternions gives a quaternion, so algebraically this is clear
How can one intuitively think about quaternions? Here is the intuitive interpretation of this Given a particular rotation axis $\omega$, if you restrict the 4D quaternion space to the 2D plane containing $(1,0,0,0)$ and $(0,\omega_x,\omega_y,\omega_z)$, the unit quaternions representing all possible rotations about the axis $\vec \omega$ form the unit circle in that plane
the logarithm of quaternion - Mathematics Stack Exchange I can't see the page in Google Books, but what you apparently have there is the logarithm of a unit quaternion $\mathbf q$, which has scalar part $\cos(\theta)$ and vector part $\sin(\theta)\vec{n}$ where $\vec{n}$ is a unit vector Since the logarithm of an arbitrary quaternion $\mathbf q=(s,\;\;v)$ is defined as
Finding the Unit Quaternion - Mathematics Stack Exchange To normalize the quaternion you do indeed divide by the norm which is $\sqrt{2^2+(-1)^2+2^2+(-3^2)}$ However, you need to divide each component by the norm rather than just the coefficients So your quaternion becomes
Combining rotation quaternions - Mathematics Stack Exchange If I combine 2 rotation quaternions by multiplying them, lets say one represents some rotation around x axis and other represents some rotation around some arbitrary axis The order of rotation ma