Rigid Body Dynamics (unconstrained)

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Rigid Body Dynamics (unconstrained) - PowerPoint PPT Presentation

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)

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

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
Uniform Force Field

No effect on the angular momentum

The Football in Flight (ref)

Gravity does not exert torque

Angular momentum stays the same

Using Quaternion

quaternion

multiplication

Unit quaternion

as rotation

quaternion derivative

Equation of

motion