Bicycle stability has been of interest to dynamicists and athletes since before J. W. Whipple described the canonical model for bicycle motion in 1899. Since then, the subject has fascinated many who sought to find a simple way to describe the essence of stability for a hands free bicycle at a prescribed forward speed. Caster and gyroscopic effects have been shown to be helpful, but not necessary for there to exist a stable range of forward speeds. This work focuses on showing how using the eigenvalues of the linearized equations for roll and steer (with and without a steering torque) can illuminate the stabilizing and destabilizing effects of changing bicycle geometry and rider position. Of particular interest is the mathematical demonstration of the decreased stability a cyclist on a time trial bike experiences when in the aerodynamic position, as opposed to riding with hands on the brake hoods or bull horns.

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