A2.6 Converting Euler Rotations to a 3×3 Matrix

The Euler notation used by Dynamic Visualizer can be simulated by building the required rotation matrix. Here are the definitions for rotations about the x, y, and z axes.

In[38]:=

Example: Rotate the object about the z axis using a 3×3 matrix.

In[39]:=

The definition of the Z-Y-Z Euler rotation may be expressed as the product of three rotation matrices.

In[41]:=

In[42]:=

Out[42]//TraditionalForm=

Using this definition, we could write a new version of EulerAngles that uses a calculated rotation matrix instead of the built-in definition of the EulerAngles rule.

In[43]:=