Am 03.10.2018 um 14:13 schrieb Kenneth:

> Going back to first principles: An object starts out as being static (that is,
> no ROTATIONS at all.) Then a force has to impinge on it to start it rotating-- a
> 'point' force for simplicity's sake. That force has a direction vector, and acts
> on the object in 3 (de-composed) vector directions, toward the center of mass.
> The magnitudes of those three vectors depend on where the force was applied on
> the surface (relative to the object's center of mass) and the angle of contact
> with the surface. If I understand the concept of 'Euler angles' correctly, those
> three force vectors can be 'simplified/combined' into just two resulting
> rotations.

No, the effect of a single force it is just a single rotation, with an
arbitrarily oriented axis.

You may have to snap out of the Euler angles picture for this. Euler
angles are good for describing "rotations" as in "transformations", but
they're of no use for properly describing "rotations" as in "continuous
motion".


To describe a realistic no-force rotation in 3D space, if you have only
Euler angles to work with, you need three angles: A changing one
describing the rotation itself, and two fixed(!) ones describing the
orientation of the rotational axis.

For a precessing motion you'd need six angles: Two fixed ones describing
the axis of precession, one changing one describing the precession
itself, another fixed one describing the tilt of the main axis in
relation to the precession axis, and another changing one describing the
main rotational motion itself. A sixth fixed angle is needed if you care
about the phase relationship between the precession and main rotation.


What you get with two changing Euler angles is a precessing motion with
a 90 degree angle between the axis of precession and the main axis, and
a fixed axis of precession (the y axis if you use `rotate <A,B,0>`).

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