Oct 19, 2010 · 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 $ …

The quaternion algebra shows there as a way of disentangling two Alamouti coded signals transmitted by a pair of antennas. The advantages come from the fact that even if the signal from one antenna is …

May 27, 2020 · Of course adding two quaternions gives a quaternion, so algebraically this is clear. I don't really think it's clear geometrically, however, and with good reason: this is a very exceptional …

Aug 5, 2015 · The idea of Hamilton was to find some generalization of this formula for three-dimensional rotations. The quaternions can do such a generalization identifying a $3D$ -vector with a pure …

Feb 3, 2017 · 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 …

Do one quaternion multiplication and you rotate the circular component just that far around, and the quaternion axis gives you the rest of the location, and the fourth dimension says how far ahead or …

Aug 11, 2014 · One of the quaternion elements is guaranteed to have a magnitude of greater than 0.5 and hence a squared value of 0.25. We can use this to determine the "best" set of parameters to use …

This is a slightly complicated question but put simply. C is the field over R such that it is of the form (a+bi) where (a,b) are in R. The quaternion is a further extension where numbers are of the form …

Jun 24, 2022 · I am trying to find a way of converting a quaternion from an arbitrary coordinate system to a fixed coordinate system that is used in my application. I have two different coordinate systems, one …

Since you are in the happy position of working with a group of small order, I think you would be well served by writing out the elements of the group, and the product of each pair of elements (including …