satellites, airplanes, spinning tops

body fixed axes and equations

Start with tranlsations and kinematic coupling terms (a.k.a. fictitious forces, pseudo forces).

Derive and name :

    F   =   m . ( x^• + ω ⨯ v )

Then go to Euler equations (with and without principal axes).

Then add motion inside the rotating frame : Coriolis terms.

Precession, nutation.