The rigidity of a system is a fundamental pre-requisite for rotating bodies that exhibit gyroscopic principles.
Is that really true?
Are ice skaters, slingshots, bolases and twirled pizza bases rigid systems?
How do they respond to torques being applied?
the conservation of AM is observed as changes in the RRPM as the blade flaps and the C of G of each blade moves towards or away from the rotor hub.
In the sense that the relative size of the torques parallel to the axis, from the hub and from drag, changes round the circle, requiring a lag on the forward-going side.
Does the fractional reduction in length from flap, by a small amount, match the fractional change in angular speed? I don't reckon it does, as the fractional speed variation is by more than the length change: which is fine, as the torque from the hub takes up the slack. There's also the issue of phasing the minimum/maximum length and maximum speed.
I'm going to keep with the conservation of angular momentum for the whole rotor-airflow system. I suggest that the angular momentum of a blade changes markedly around the circle, with couples from the hub and the airflow (which are not in the same direction) making it so, and indeed, making it flap.
As for Cierva - if you read deeper you will know that while the flapping hinges prevented the undemanded rollover - the dragging hinges prevented the lead-lag loads destroying the blades at the root - therefore equally clever
Absolutely. Would you agree that the undemanded rollover was avoided by the hinges allowing the "hub" - the whole autogyro - to tilt somewhat independently of the blades?