Now you have a quad engine rocket propelled _brick_ flying by thrust only, no aero dynamics involved at all.
Technically, aerodynamic principles govern the conversion of temperature and pressure in the combustion chamber into exhaust velocity as the propellant travels through the nozzle.
Now to the helicopter: it does not fly by thrust at all, with "thrust" it it only gets its "directions", its lift it is getting from the profile of its "moving wings" in the rotor. Thrust it gets from the tilting of the rotor as the rotor creates a minimal amount of thrust in addiction to its lift.
Actually, helicopter rotors are typically symmetric, meaning they produce zero lift/thrust at zero angle of attack. The amount of lift/thrust they get is directly dependent on the pitch of the rotor blades, and the "profile" or camber of the blades is only to prevent flow separation on the suction side of the blade at higher angles of attack.
You mention the "tilting of the rotor", which I suspect is a serious misunderstanding of how a helicopter works. Helicopter rotor blades pitch up and down to produce more or less lift/thrust, but the rotor disk itself does not move in relation to the attitude of the helicopter The disk is fixed. If the helicopter wants to move forward, the entire craft, rotor disk, fuselage and all must pitch forward to change the direction of thrust.
It pitches the swashplate such that the rotor blades currently at the front of the disk have a low or negative angle of attack, while those at the back have a high angle of attack. This shifts the center of lift/thrust rearward with respect to the center of mass, causing the helicopter to pitch forward. Now that the whole craft, including the rotor disk, is pitched forward, the lift/thrust vector tilts rearward, and the rotor now produces forward thrust.
A quadcopter uses _only_ the thrust of its engines/propellors
Just how does a propeller work, if not aerodynamically?