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.
State vector of a single particle
Change of Y(t) over time
Solved by any ODE solver (Euler, Runge-Kutta, etc.)
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
Three columns of R(t) correspond to the axes of the body-space in the world spaceThe Rotation Matrix
How are R(t) and body-space in the world spacew(t) related?Linear and Angular Velocity
Single particle body-space in the world spaceLinear Momemtum
No effect on the angular momentum
Gravity does not exert torque
Angular momentum stays the same