The disc can't flap to equality when the cyclic position prevents it from doing so. Doesn't mean it isn't trying to.
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I know it is some time since many of us looked at the books, but.... the tip path plane is only partly directed by the cyclic, it is otherwise determined by the flapping resulting from translation of the rotor disk through the air. While flapping alters the TPP, it doesn't add significant rolling moments to the hub (it isn't perfectly isolated though, there are some relatively small consequences). The effect of flapping from the translation is to balance forces, and the cyclic adds an additional force that causes the TPP to alter, and where there is a hinge moment, to develop a roll or pitch moment to the body of the helo, and with zero hinge moment, for the motion of the disk to lead to a moment from the center of the disk to the CG of the helicopter, which then moves the body in lag to the disk.
The cyclic doesn't alter the flapping of the TPP resulting from translation, which is resulting in varying velocity of the advancing and retreating blades. The cyclic is additive to the flapping response, as is shown in the Fourier series that describes the TPP. theta sub 1c is lateral cyclic pitch angle, theta sub1s is longitudinal cyclic pitch angle, and theta subo is the collective pitch angle. beta gives the flapping... zeta is the in plane lead lag, gamma is the lock number (the relationship of aerodynamic to inertial response of the rotor blade).
There is a wealth of really good reading for helicopter drivers out there, stuff that actually tells it as it is, gives the equations of motion, derivatives etc, and which (for my money) is well worth the coin for any helo driver. I do fundamental aerodynamic flight testing in helicopters and jet aircraft, as well as prop planes, and the helicopter is the one that I take the most care over, by far; I respect the courage of young helicopter CFIs that go out and teach engine failure OGE to a zero time student in an R-22, they are braver than I am... knowing the maths is not necessary to fly a helo, but knowing the science (the equations) is worth the effort if you go and play on the periphery of the envelope. The beauty of the helicopter and the reason I love flying them is that they are brutally honest, they show what the pilot is doing instantaneously, more than a Pitts S1 does.
Suggested reading list:- Principles of Helicopter Aerodynamics J Gordon Leishman.
- Helicopter Aerodynamics Vol 1, Vol 2, Vol 3 Ray Prouty
- Helicopter Performance Stability & control Ray Prouty
- Basic Helicopter Aerodynamics John Seddon & Simon Newman
- Aerodynamics of the Helicopter, Alfred Gessow & Gary C Myers Jr
- Helicopter Theory, Wayne Johnson
- Rotorcraft Aeromechanics Wayne Johnson
- Rotary-wing Aerodynamics W.Z. Stepniewski & C.N. Keys
- Helicopter Flight dynamics Gareth Padfield
- Practical Methods for Aircraft and Rotorcraft Flight Control Design: An Optimization-Based Approach, Mark B Tischler, Tom Berger, Christina M Ivler, M H Mansur, K.K. Cheung, J Y Song
- Cyclic & Collective, Shawn Coyle
- The Art and Science fo Flying Helicopters, Shawn Coyle
- The Little Book of Autorotations, Shawn Coyle
....
and something written by the FAA.
Shawns work is easy reading and a good operational input. Rays stuff is also relatively easy to get into, and it is worth having in hard back, (I've worn out a couple of copies). Gessow and Myers dates back to 1952, and not much has changed, Ch 7 is worth reading there, and it is consistent with Prouty, Johnson Stepniewski & Keys, and Leishman. (I like Johnsons work, he looks at each state from various analysis and that gives a helpful overview). Gessow and Myers work is available as a PDF, and is still relevant but does use some nomenclature that has fallen from favour in later works, the physics remain the same.