Rigid Body Motion
Description of rigid body motion.
Moment of inertia tensor.
Euler angles, Euler equations of motion
Components of angular velocity with respect to body axes
The total angular momentum about a point O is equal to the angular momentum of motion concentrated at the center of mass, plus the angular momentum of motion about the center of mass
Definition of Moment of Inertia
“Parallel Axis” Theorem
The moment of inertia about a given axis is equal to the moment of inertial about a parallel axis through the center of mass plus the moment of inertia of the body, as if concentrated at the center of mass, with respect to the original axis
Parallel Axis Theorem for Moments of Inertia
Principal values of moment of inertia
The inertia tensor
I and all the quantities associated with it—principal axes, principal moments, inertia ellipsoid, …, are only relative to some particular point fixed in space.
If the point is shifted elsewhere in the body, all the quantities will in general be changed.
Motion of symmetric top: body-fixed frame
Torque free rigid body motion
Precession of angular velocity about axis of symmetry
Heavy Symmetrical Top
Heavy Symmetrical Top: One Point Fixed
Turning angles of top on horizontal surface
Possible shapes for locus of figure axis of top