ECE 417 --- ROBOTICS
Homework
1, Spring 2021
For the rotation matrix:
^{XYZ}R_{UVW} = |
[ |
2/7 |
-6/7 |
3/7 |
] |
6/7 |
3/7 |
2/7 |
|||
-3/7 |
2/7 |
6/7 |
Show that ^{XYZ}R_{UVW } is a proper rotation matrix.
Show that R^{-1} is equal to R^{T} where (R is shorthand for ^{XYZ}R_{UVW}). HINT: taking the inverse is not required.
Compute R A where matrix A is given by
A = |
[ |
3/7 |
2/7 |
6/7 |
] |
2/7 |
6/7 |
-3/7 |
|||
-6/7 |
3/7 |
2/7 |
If P_{UVW} = (1,2,3)^{T}, what is P_{XYZ} given (using ^{XYZ}R_{UVW} above)
If P_{XYZ} = (1,2,3)^{T}, what is P_{UVW}? given (using ^{XYZ}R_{UVW} above)
If the OUVW system has basis vectors U = (1/√2, 0, 1/√2)^{T}, V = (-1/√2, 0, 1/√2)^{T}, W = (0, -1, 0)^{T}, and the OXYZ system has basis vectors X = (1, 0, 0)^{T}, Y = (0, 1/√2, -1/√2)^{T}, Z = (0, 1/√2, 1/√2)^{T}, then what is the corresponding rotation matrix between the two systems?