7.1 Extracting Euler angles from a rotation matrix

7.1 Extracting Euler angles from a rotation matrix

We discussed different angle set conventions in class. One common convention is the set of X-Y-Z Euler Angles. With this convention, the B frame is first rotated about 

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by angle
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, then rotated about
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 by angle
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, and then finally rotated about
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 by angle
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. This angle set has the following form.


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Using the examples from class as a primer, and using the atan2 function, please derive the formulas necessary to extract the values of angles

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, and
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 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 (
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,
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, etc.) and clearly state any assumptions that you make.


 Solution (only visible by instructors; please contact us to request access)

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