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^AR^B_{X' Y' Z'} ( \alpha, \beta, \gamma) = \left[
\begin{array}{ccc}
\dfrac{5}{6} & \dfrac{1}{6} & 0c \beta c \gamma & - c \beta s \gamma & s \beta \\
s \alpha s \beta \dfrac{5}{6} & 0 & \dfrac{1}{6}c \gamma + c \alpha s \gamma & - s \alpha s \beta s \gamma + c \alpha c \gamma & - s \alpha c \beta \\
0- c \alpha s \beta c \gamma + s \alpha s \gamma & \dfrac{5}{6} c \alpha s \beta s \gamma + s \alpha c \gamma & \dfrac{1}{6}c \alpha c \beta
\end{array}
\right] |
Using the examples from class as a primer, and using the atan2 function, please derive the formulas necessary to extract the values of angles , , and f rom , and from the above rotation matrix. For simplicity, you may assume that no angles equal either 0° or 90°. Please express your answers in terms of elements of the rotation matrix (r11, r23| Mathinline |
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| body | --uriencoded--r_%7B11%7D |
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, | Mathinline |
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| body | --uriencoded--r_%7B23%7D |
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, etc.) and clearly state any assumptions that you make.
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| S7.1 Extracting Euler angles from a rotation matrix |
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| S7.1 Extracting Euler angles from a rotation matrix |
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