What is the rotation matrix R? Is it like our 2D rotation matrices where it is
\begin{bmatrix}
cos(theta) & -sin(theta) & 0 \
sin(theta) & cos(theta) & 0 \
0 & 0 & 1 \
\end{bmatrix}
are the 0's and 1's filled in for a 3d rotation matrix? I can't find a lot of information about this matrix.
Sorry above I tried to write it out in latex form but what usually works for latex in overleaf for matrices doesn't seem to translate well to this site. I was trying to represent a 3x3 matrix above.
mpotoole
The rotation matrix around the Z-axis is given by your matrix:
The wiki page on rotation matrices also describes the corresponding matrices for rotation about the X-axis, Y-axis, and even rotation about an arbitrary axis.
I'll also point out a couple of useful properties for rotation matrices $R$. First, it is unitary, i.e., $R^TR = R R^T = I$. Also, it's determinant is equal to 1, i.e., $det(R) = 1$. Third, the eigenvalues of $R$ are all 1s.
What is the rotation matrix R? Is it like our 2D rotation matrices where it is \begin{bmatrix} cos(theta) & -sin(theta) & 0 \ sin(theta) & cos(theta) & 0 \ 0 & 0 & 1 \ \end{bmatrix} are the 0's and 1's filled in for a 3d rotation matrix? I can't find a lot of information about this matrix.
Sorry above I tried to write it out in latex form but what usually works for latex in overleaf for matrices doesn't seem to translate well to this site. I was trying to represent a 3x3 matrix above.
The rotation matrix around the Z-axis is given by your matrix:
The wiki page on rotation matrices also describes the corresponding matrices for rotation about the X-axis, Y-axis, and even rotation about an arbitrary axis.
I'll also point out a couple of useful properties for rotation matrices $R$. First, it is unitary, i.e., $R^TR = R R^T = I$. Also, it's determinant is equal to 1, i.e., $det(R) = 1$. Third, the eigenvalues of $R$ are all 1s.