Hello
Before I "phrase" my question (and that may be my problem), may I first state what I do know.
I understand that a Rotation matrix (a member of SO(3)) has nine elements.
I also understand that orthogonality imposes constraints, leaving only three free parameters (a sub-manifold)
I also...
Homework Statement
so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3, I've uploaded the page here
The rotation matrix associated with 1.2a and 1.2b is
\begin{pmatrix}
\cos\theta &...
I envision the three fundamental rotation matrices: R (where I use R for Ryz, Rzx, Rxy)
I note that if I take (dR/dt * R-transpose) I get a skew-symmetric angular velocity matrix.
(I understand how I obtain this equation... that is not the issue.)
Now I am making the leap to learning about...
Say I have {S_{x}=\frac{1}{\sqrt{2}}\left(\begin{array}{ccc}
0 & 1 & 0\\
1 & 0 & 1\\
0 & 1 & 0\\
\end{array}\right)}
Right now, this spin operator is in the Cartesian basis. I want to transform it into the spherical basis. Since, {\vec{S}} acts like a vector I think that I only need to...
First, I'd like to say I apologize if my formatting is off! I am trying to figure out how to do all of this on here, so please bear with me!
So I was watching this video on spherical coordinates via a rotation matrix:
and in the end, he gets:
x = \rho * sin(\theta) * sin(\phi)
y = \rho*...