Then try doing it at night
It is midnight, mid-winter in the North Atlantic in a Force 10 storm. I am sitting in my Wasp perched atop the hangar/flight deck of HMS Tartar. I am lashed to the deck and the swivel link is on, but my AI is telling me that the ship, a Tribal Class designed for the Gulf and without stabilisation, is rolling more than 20 degrees to port and starboard. My rotor disc follows the movement of the ship exactly and I need to make no control movement, except that I push down on the collective and through the detent to remove the last 2 degrees of pitch and cling even more tightly to the deck.
The AI is a gyroscope; the rotor is not.
There is no thrust from the rotor and no blade produces any thrust at any point in its path.
I trim the cyclic forward and the tip-path-plane tilts down. The blades are flapping cyclicly.
There is no thrust from the rotor and no blade produces any thrust at any point in its path.
Explain this and you will have explained why an 'ideal' articulated rotor has 90 degrees phase lag. You will also be able to give an indication of why offset hinges, delta hinges etc reduce the phase lag. You will do this without any mention of gyroscopes, gyroscopic effect or gyroscopic precession.
Of course, this will be a 'simple explanation' of the gross behaviour of a rotor in quasi-steady-states. It will not explain the behaviour in transitory states, when I fully expect the dynamics of rotating masses, 'gyroscopic effects' if you like, to be important.