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Rigid Body Dynamics (unconstrained)

Rigid Body Dynamics (unconstrained). Simulation Basics. State vector of a single particle. Change of Y(t) over time. Solved by any ODE solver (Euler, Runge-Kutta, etc.). Body space Origin: center of mass p 0 : an arbitrary point on the rigid body, in body space.

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Rigid Body Dynamics (unconstrained)

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  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. 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) Rigid Body Concepts

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

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

  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

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