I'll give it a start with an frightfully unsubstantiated perception:

While the pendulum effect (i.e. a low CG) creates a momentum towards a defined AOA, it also builds up energy when rotating (i.e. inertia) which probably make tumbling more probable and (if it happens) ferocious. Can this effect be quantified?

Let me try to help out with this whole suggestion that the CG can swing under the wing like a pendulum.

First concept to get straight is the airplane moves, both in translation and in rotation. Translation is movement in a straight line, usually defined in longitudenal, vertical, and lateral directions. Yeah, the direction the ship is pointed, the up-down direction, and the left right direction. Rotation is the classic pitch, yaw, and roll axes.

Fly the airplane and translations of the CG and rotations about the CG occur.

In steady state flight, the translations occur steadily while forces and rotation are zeroed out.

Now if you want to start accelerating the beast, you have to make one or more forces unbalanced. To accelerate in the longitudenal axis, either drag must be reduced or thrust increased, and the unbalanced Force will accelerate the mass of the ship. Equation that let's you figure out acceleration is F = m*a. If you know the unbalanced force F and mass m, do the algebra and F/m = a.

We have an equivalent equation for rotation. M = I*alpha, where M is an unbalanced moment in one of the axes, I is the mass moment of inertia about the CG, and alpha is rotational acceleration. Want to know alpha? Do the algebra, and alpha = M/I.

If this is a nose up moment, then the airplane will pitch up. As the AOA increases the lift increases and the airplane starts to describe a loop. If there is enough kinetic energy in the longitudenal direction plus enough extra energy added by thrust, the loop will proceed. But in the process, you have also put energy from someplace into rotation in the pitch axis. Here, KErot = 1/2*I*omega^2 where I is the same mass moment of inertia in pitch axis about the CG, omega is rotation rate in radians/sec. you also have rotation momentum, MOMrot = I*omega.

How do we get that pitching moment and rotation? If you slowly add nose up elevator, the airplane will slowly increase nose-up angle and slow down, and approach stall. If instead we move the controls vigorously to the stop for pitch up, we can get some rotation speed and the nose could go through the stall AOA, and perhaps get into deep stall. Do this fast with a footfull of rudder and it snap rolls. This is all very normal.

One other thing is going on. If the controls, applied slowly and smoothly and then held at a position would have produced a particular attitude and AOA of the airplane, the airplane would have been balanced at that attitude. If you somehow dynamically got it to overshoot the stable spot, most of the time there is now restoring moment resulting that is trying to slow rotation and return the airplane to its stable spot for this state of the controls. If instead of returning toward the original stable position, we get rotate on through to a deep stall or a spin that stays without rudder inputs, that is bad. Enough rudder and elevator to stop yaw rotation and then break the stall is required to get back out of this case.

Can it be quantified? You bet. You do a time step integration of the state of the airplane in three translation and rotation axes (both positions and accelerations), with wing and control surface characteristics, and masses and mass moments of inertia included and you can simulate all of this. The Control and Stability texts get into all of this stuff.

Now where does this "pendulum" come in? The CG is translating and then the airplane is rotating about the CG. A high wing airplane with the CG below the wing is then moving the mass of the wing aft, any object ahead is moving up, and objects behind are moving down, and the mass of the landing gear is moving forward. If this is what you meant by a pendulum, well, let's use the established nomenclature for mass moment of inertia, rotational velocity, rotational momentum and, rotational kinetic energy.

And if that is not what you were attempting to describe, well, maybe a little more effort to explain all of this is needed.

Billski