RE: [Flightgear-devel] Turn ball fix & JSB notes

[BERNDT, J. S. (J. (JSC-E. (LM) <jon...@js...>]

> But the derivation is trivial:

Yes, as I looked over the math I realized I had done this many times ...
just not for a while. :-)

> 1 Calculate the aerodynamic force in the body frame.

plus propulsion, plus gravity, plus gear, plus centripetal ...

> 2 Transform to the geocentric frame, and use it to calculate an
>   acceleration in that frame using the F=ma relation.  This
>   transformation is just a rotation and translation, so it's legal.
>   The force you get will still be valid in the earth frame.

OK, so we have a set of forces and moments in body coords and a set of Euler
angles. I am still not clear on the conversion to geocentric. I'll have to
find some time to look that one up.

> So that's the reason the patch looks complicated.  It's undoing the
> damage done by McFarland's funny terms.  Again, the problem is not
> that JSBSim is generating bad answers for simulation questions.  It's
> generating the right answers, because McFarland's terms are correct.
> The problem is that because of the non-inertial reference frame, you
> can't assume that the acceleration felt by the pilot (which obviously
> depends only on physics and not on the characteristics of the
> reference frame it's measured in) is the time derivative of velocity.
> Acceleration is equal to V-dot ONLY in inertial reference frames.

Right. So, again, the equation for acceleration would be, in words:

The acceleration of a point in space that is attached to a moving coordinate
frame itself, in inertial coordinates, is the acceleration of the origin of
the moving frame plus w X (w X R) plus wdot X R. "w" is the rotational
velocity of the moving frame.

After the acceleration is found, then, it would have to be converted to body
frame.

Jon