Linear Algebra 21i: How to Represent a Rotation with respect to an Arbitrary Axis

[shravilpotdar]

Such a simple and awesome explanation, I was scratching my head before I landed here.
Thanks! :)

[jayadevreddy]

Awesome!!! I have been trying really hard to understand equivalent axis representation for my robotics course, but this is the first video that made me understand it clearly. You are truly an awesome teacher.

[tomazws]

omg why can't my university have you teaching my class???? You explained everything so easily to understand within 10 mins.

[_ahmadyazidnaufan]

Just want to point something, that rotation method could only be done if the arbitrary axis is exactly pass through origin point. elsewhere there is an additional steps to translate the arbitrary axis in order to pass through origin point and then re-translate it back after core rotation step has been done.

[WowPlusWow]

Why does the vector have to be translated to the z axis and then rotated? Why not the y or x axis?

[joshuaronisjr]

Awesome Thank you. I have a question:
Let's say the axis we want to rotate around is given by a vector with components in the X, Y, and Z directions instead of degrees of rotation from some (in this case the Z and Y) axes. How would we rotate another vector (or some object) around this arbitrary vector (axis)?

[Romandangal]

how to determine phi and theta
and why y and z rotation why not x and z

[tangolasher]

+MathTheBeautiful Thanks so much! By the way, how can you apply the same angles / matrix transformations to both the object being rotated and the axis of rotation? This connection doesn't feel very clear to me, and it doesn't seem at all obvious that the object automatically "comes along with the axis." Because the axis of rotation feels more like the "basis" for the rotation, but the object is the thing being transformed within that basis, unless I'm mistaken. Thanks again.

[xueqiang-michaelpan]

Does R(-theta)R(-phi) commute in this operation?