Le_Forgeron <jgr### [at] freefr> wrote:

> >
> It's not the size which matters, it is how you use it.

LOL!
>
> composing rotations might not be what seems natural, especially when
> they are done along fixed axes. Euler's angles have moving axis: the
> first rotation is from the base(x, on z), but the second is from the
> updated vector (on updated x), and so is the third (on updated z) which
> in part compensate for the first one.

Yes; that seems to be the primary idea and reason for Euler's mathmatical
invention.

>
> To summarize:
> you need 3 angles (in Euler's system) to describes any orientation, but
> natural fall would only change two angles during animation and such
> change would be with a null second derivative for each unless you have
> friction or engine in play.

Yeah! That's what *I* think :-)
(...as I thumb through my calculus books with a quizzical look on my face...)

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