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

Explore the intricacies of Euler angle simulation using MATLAB in this comprehensive lecture on space vehicle dynamics. Delve into the kinematic differential equations to understand how time-varying angular velocity affects rigid body orientation. Learn to numerically integrate these equations using the 3-2-1 Euler angle convention, commonly known as yaw-pitch-roll in aerospace. Follow along with a detailed MATLAB tutorial that demonstrates the simulation process, including visualization using the Space Shuttle as an example. Gain insights into various attitude coordinates, such as Euler parameters, modified Rodrigues parameters, and quaternions. Enhance your understanding of rigid body kinematics, rotation matrices, and the topological representation of Euler parameters in N-dimensional spheres.

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..