Giovanni Amelino-Camelia, "Doubly-Special Relativity: First Results and Key Open Problems." Int. J. Mod. Phys. D11 (2002) 1643. Online copy at http://arxiv.org/abs/gr-qc/0210063
... fall over, but start precessing around. (The precessing motion is perpendicular to the torque trying to make the gyro fall over.)
The axis of the gyroscope in the ...