1. P. V. Buividovich,
The inertia tensOR

2. Angular momentum of a rigid 3d body
Inertia matrix,
In fact, INERTIA TENSOR
In general, L is not parallel to w
=> Precession of 3D bodies!

3. Kinetic energy of a rigid 3D body

4. Rotations of a reference frame
Inertia matrix is a tensor
Inertia tensor itself “rotates” in lab frame
(Again precession)
Frame of principal axes rigidly attached to body – inertia matrix diagonal
Principal axes are axes of symmetry

5. Shifts of a reference frame
Total mass and center of mass
Inertia tensor of a point with mass M
It is advantageous to calculate the inertia tensor
with respect to the center of mass (ρ = 0)

6. Inertia tensor of a solid brick

7. Teaser for the next topic: Dzhanibekov effect

8. Precession: mathematics
Euler equations
In body frame, w rotates, precession!