FooTheBar:
"When you're spinning these flywheels you're going to get a tremendous gyroscopic effect that would make the quadcopter impossible to maneuver."Of course, but this is also true for each of the rotors on your quadcopter
One possible solution is to use two flywheels with the same speed and shape but with different directions. (i.e. exactly the same solution you use for your quadcopter)
I am curious how you will get the fly wheel to spin? If you use a power source, not only will you add unnecessary weight to the quad, but you are also adding inefficiency to your project. Why would you use power to spin a flywheel to make power?? Even if the system was 99% efficient (which it wouldn't even be close to), you are still using more power than you are making. Cars that utilize a fly wheel, such as a KERS system, capture small amounts of power from braking that would otherwise be lost as heat. What quad system is analogous with the braking system of a car?? I can't think of one, but that doesn't mean one doesn't exist. What are your thoughts on this issue?