I think you have invented something cool and useful, but it is not a stabilization system. It is a way to allow the forward fins to not contribute as much to the Cp because they pivot to allow air to flow around them.
Lets think about forces. You can break down the forces on a rocket into gravity, thrust, drag, and normal force. There are lots of guides and technical reports with diagrams and discussions. The treatment and pictures in Sampo Niskanen's documentation for open rocket:
http://openrocket.sourceforge.net/techdoc.pdf are clear and easy to follow. This is on p. 24 of the pdf or p. 15 of text.
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Gravity is a sneaky one. If you hold the rocket in your hand, like in
post #60, gravity does make the fins turn. However if you take away your hand, and motor thrust, and air, and let the rocket fall freely the fins will not turn because every component of the rocket will fall with the same acceleration. So this isn't going to help with stabilization.
Next we have thrust and drag. When the motor is powered up, the rocket is pushed with something like 5 to 20 gs of acceleration. Then the motor burns out and atmospheric drag decelerates the rocket body. Think of what happens with the
gravity assist pendulum hooked to your fins under these conditions: during acceleration and deceleration the forces on the pendulum and hence fins is opposite. They can't both be stabilizing.
Finally we have the atmospheric normal forces, aka lift. Your fixed fins at the aft end of the rocket are contributing to Cp. The pivoting fins (with their axel above the fin Cp) allow the fin to twist to be parallel to the airflow. These fins will make a little drag, but their pivoting prevents the kind of lift that went into the Barrowman equations/cardboard cutout model/every simulation program. Cn -> 0 as alpha -> 0. The Cp that is produced by these methods assumes rigid, not pivoting fins. Take your cardboard cutout model and twist the two big middle fins so you are looking at their edge. That is what they look like to the wind. There will be a small drag force, but it is applied to the rocket body through the fin axel, which is almost right at the Cg, so it will apply a little drag and negligible torque to the rocket body.
The cool thing is that by allowing the large midsection fins to pivot, they don't contribute to Cp and don't destabilize the rocket if they are near or behind the Cg. You can use this to make some cool rockets that are not otherwise possible.
You are probably better off omitting the pendulum weight entirely and just using a straight axel. The pendulum isn't helping. It is being overwhelmed by the atmospheric forces twisting the fins. Put its mass into the nose cone instead.