David,
I'm going to respectfully disagree with the author of AN4070 on the topic of "rotational freefall". I would like to refer you to a blog posting I created some time back at Accelerometer placement - where and why. Equation 15 at the end of that posting is:
Ar' =A + Ar + <-- Inertial Acceleration
2ω X Vr + <-- Coriolis Acceleration
α X r + <-- Euler Acceleration
ω X (ω X r)) <-- Centripetal Acceleration
I'll refer you to the original blog posting for definitions of terms. The important point is that AN4070 was attempting a Heuristic approach to detecting rotational free fall that does not consider the full implications of the equation above. A single accelerometer cannot by itself separate all the effects shown in the equation. You need to either add additional sensors or restrict the types and/or ranges of motion you are considering. I would not spend any more time pursuing the AN4070 rotational free fall approach, and I'll be recommending that AN4070 be updated and/or removed from the website.
As to your second question, since there is no force, and therefore no acceleration other than gravity, on your sensor once it leaves your hands, I don't see an easy way to differentiate the peak from the rest of the trajectory. You would have to compute the initial vertical velocity & acceleration of the object based upon accelerometer data prior to release, then figure out how long in free fall you need to reach 0m/s at the top of the arc. Very tough to do for the general case. Maybe someone else is more clever than me...
Mike
12/31/2014 4:44PM Addition: David,check out AN4446, which addresses determining the high point of the trajectory.
