2.3 Rotations in 3D

In this lecture, I extend the 2D rotation matrix of SO(2) from Lecture 2.2 to SO(3). Rotation matrices can be constructed from elementary rotations about the X, Y, and Z axes. I also cover the problem of Gimbal Lock, and how to express rotation error.

[alevsahin]

Thank you! You saved my life with that explanation 😭 I have exams in a week, wish me luck!

[jargok]

The rotation direction of y axis is wrongly shown. It shouldn't be clockvise in this view. I think this may lead to confusion.

[McLachlanG]

Hi, I believe the pitch rotation (about the y-axis) may be illustrated incorrectly. A positive pitch rotation should rotate a vector downwards. I.e., a rotation of pi/2 will rotate a vector pointing straight forward [1, 0, 0] to straight down [0, 0, -1].

[MiguelGonzalez-mthv]

Why is the positive theta angle for the y axis not in the same direction as the x or z axis (following the right hand rule)

[ajit_edu]

2.39 i am confused about the direction of rotatiin. Should not they be in opposite direction at x and y axis?

[rimene]

That was really helpful. Thank u sir simple and clear. Thanks u 🙏

[Shadow]

How do we calculate a second rotation? For example, after a body pitches 45 degrees, it yaws 45 degrees about its body frame? It would be incorrect to multiply its nose vector, say <1, 0, 0> by R(y=45 deg) * R(z = 45 deg), since the second matrix that you would be multiplying by is in the inertial (unrotated) frame.

[amr.a-m]

Good video .How I could substitute Phi =2tan(R23, R33)as function of number elements please & extracting 'Jacobian Matercis' from rotation matrix.

[markkennedy]

Is there any geometric/visual way of seeing why every rotation is a composition of two rotations.

[MonirulAhmed]

using matrix find the transformation equation for a 90° degree rotation about the z axis of cartesian coordinate system

[joseluiz]

At minute 7:01, you're showing how to extract the angles from the matrix, but using Z, Y, X orientation right?

[armanmotamedi]

you positive y rotation vector is wrong. It is the other way. You are showing a negative pitch. Keep you thumb along positive y axis.

[mariaph]

At 2:55, would you mind explaining why there is a difference in sign of rotation matrices of x, z with y?

[er]

It seems R(z) is a rotation clockwise instead of conterclockwise. Is that correct?

[satyamshrivastav.]

I have doubt, Can you please explain how 0 .97 was came, in your example problem.

[paaabl.]

Is counterclockwise direction of rotation arbitrary?

[xCOUZIAx]

In illustration 2:30 to 3:15, the direction of rotation is wrong for the y-axis :)

[punstress]

I have been following the other videos but this one confused the heck out of me.

[enjieruuu]

Can you help me with an exercise please 😭🙏🏻🙏🏻 I've been struggling for 2 days with just having to give the homogeneous transformation matrix Thank you very much in advance 🌻 It’s a graded practical exercise 🙏🏻🙏🏻😭

[MonirulAhmed]

find the transformation equation for a 90° rotation about the z axis