This is a rather interesting paper that investigate the stability of riding a bicycle on rollers. The bicycle isn't moving, but the wheels are still turning. So if one thinks that the stability in riding a bicycle is due mainly to conservation of angular momentum of the wheels, this is a very good test because here since the motion isn't there, but the wheels can still turn, thus preserving the angular momentum.
So what do they observe?
Riding a bicycle on rollers is unique because of the absence of the forward inertia which aids in bicycle handling for stability, instead of isolating and restricting the degrees of freedom in handling. Adopting one’s riding style to ride on rollers is quite difficult, with many avid cyclists falling off their bicycles on the first few attempts. Given that all riders struggle somewhat with the apparatus, but some more than others, the degree of struggle to ride on rollers may also indicate how different riders rely on specific factors for bicycle stability, which has not been addressed in many studies up to now. We use the example of riding bicycles on rollers as a test case on the individual factors that lead to bicycle stability.The paper gives quite a few references to various treatment on the issue of stability on bicycles.
 P.A. Cleary and P. Mohazzabi, Eur. J. Phys. v.32, p.1293 (2011).