Clear Explanation of Euler Angles with Animation, Rotation and Cosine Matrices, and Python Code

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In this aerospace and robotics tutorial, we explain one very important topic for properly understanding the kinematics and dynamics of rigid bodies. We explain the concept of Euler angles. In particular, we explain the so-called Z1-X2-Z3 Euler angles. We will first graphically explain the Euler angles, and then we will derive the expression for rotation matrices and direction cosine matrices that are the consequence of Euler rotations. We will also present the Python code that can be used to compute the direction cosine matrix of the associated Euler rotations.

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