Euler Angle Simulation with MATLAB - Integrating the Rotational Kinematic Differential Equations

This course demonstrates how to simulate a rigid body's orientation under time-varying angular velocity by numerically integrating 3-2-1 Euler-angle kinematic differential equations in MATLAB. It includes plotting the angles, visualizing rigid-body motion in 3D, and introducing Euler parameters and quaternions.

Syllabus

Kinematic differential equation review.
MATLAB demo introduction.
Writing ODE function with kinematic differential equations.
Numerical integration of ODE function of Euler angles.
Plotting the results.
3D visualization of resulting rigid body motion.
Challenge for the student: use Euler parameters instead of Euler angles.
Other attitude coordinates: modified Rodrigues parameters, stereographic projection, Cayley-Klein parameters.
What the Euler parameters topologically represent, and spheres in N dimensions.
Typical quaternion notation is different. The Euler parameter set, also known as a quaternion, is a four-parameter set..