1. Rigid Body Dynamics (unconstrained)

2. Simulation Basics State vector of a single particle
Change of Y(t) over time
Solved by any ODE solver (Euler, Runge-Kutta, etc.)

3. Rigid Body Concepts Body space
Origin: center of mass
p0: an arbitrary point on the rigid body, in body space.
Its world space location p(t)
Spatial variables of the rigid body: 3-by-3 rotation matrix R(t) and x(t)

4. The Rotation Matrix
Three columns of R(t) correspond to the axes of the body-space in the world space

5. Linear and Angular Velocity
How are R(t) and w(t) related?

6. R(t) and w(t)

7. R(t) and w(t)

8. Velocity of a Particle

9. Force and Torque

10. Single particle
Linear Momemtum

11. Center of Mass

12. Angular Momemtum

13. Inertia Tensor

14. Inertia Tensor

15. Equation of Motion

16. Inertia Tensor of a Block

17. Inertia Tensor Table (ref)

18. Uniform Force Field
No effect on the angular momentum

19. The Football in Flight (ref)
Gravity does not exert torque
Angular momentum stays the same

20. Using Quaternion quaternion multiplication Unit quaternion as rotation
quaternion derivative
Equation of
motion

21. Computing Qdot