P. V. Buividovich, The inertia tensOR.

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Presentation transcript:

P. V. Buividovich, The inertia tensOR

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!

Kinetic energy of a rigid 3D body

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

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)

Inertia tensor of a solid brick

Teaser for the next topic: Dzhanibekov effect

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