Quaternions

[BXMATTER]

Never in the history of man has anyone explained quaternions in such a simple manner.

[xandergerrmann]

I really liked this video. It builds up perfectly.

[a.j.o.manalansan]

I'm confused how quaternion (1/sqrt(2), 1/sqrt(2), 0, 0) only rotates at the pitch axis by 45deg.

Isn't it supposed to be:
Roll by pi/2, and pitch by pi? Because if we convert that quaternion into the axis angle:
Theta = Pi/2
V1 = 1.0
V2 = 0.0
V3 = 0.0
Which tells us that the object is pitching at Pi(1, 0, 0) and rolling at Pi(theta = pi/2)

[timelsen]

Harr measure by using quaternions gives cosets of the same size as the set for any multiplier which applies to the complex plane too. So for the set πr^2 it's said 2 times this set when multiplying radius is not Harr measure as becomes 4 times the area. Seems for the group cosets translation is additive and wanted not multiplying! Translating the radius to an annulus would scale in a factor of 3 at r to 2r so still not a Harr measure.

This is interesting with the distributions over the quaternions for monte Carlo methods giving uniform representation of rotation spaces, while Euler angles have gimbal lock.

Wish someone could further explain this to me.
Great lecture though.

[monkeith]

Great video! This is the most simple yet very useful video about quaternion I have ever found. Just one thing, if my movement is pitch by 30 deg yaw by 120deg and roll by 50deg simultaneously, how can I get the angle or theta to be used for cos theta/2? Hope you'll find time to answer, thanks. Btw, new subscriber here.

[FreakyStyleytobby]

Comon, don't put this kind of shit audio in the next videos. The video is great, and prof is talking interesting stuff, but the audio makes it hard to watch.

[englishforfunandcompetitio]

You're not in the business of defining and introducing Quaternion. You do not apply an intuitive approach towards the main objective of introducing this complex concept. You rather apply Quaternions to some problems in your field of interest. Your lecture doesn't serve the purpose.