1p) Astrom, K. J., R. E. Klein, et al. (2005). Bicycle Dynamics and Control: Adapted bicycles for education and research. IEEE Control Systems Magazine. 25: 26-47.

2p) Lowell, J. and H. D. McKell (1982). "The Stability of Bicycles." American Journal of Physics 50(12): 7.

3p) Jones, D. E. H. (1970). The Stability of the Bicycle. Physics Today. 23: 34-40.

This is probably the most famous piece written on bicycle stability. Almost every paper on the subject references this article. Jones may have been the first person to show the connection between front fork geometry, namely trail, and the inherent stability of the bicycle in an article suited to the layman. Whitt and Wilson [3b] give a great summary of Jones' paper and add more information than is in the paper itself.

Jones built several experimental bicycles to prove and disprove some theories. His first bicycle was configured so that the gyroscopic forces from the front wheel were canceled. The bicycle was easily ridden hands-on, difficult to ride hands-off and showed no signs of self stability when released riderless. One experimental error that may have been introduced to the first bicycle configuration was that the counter rotating wheel was hung off the side of the fork, thus creating moment about the steering axis. Better designed gyro cancellation bicycles can be found in [1p].

The second bicycle configuration had increased trail due to the fork being rotated 180 degrees. This bicycle was awkward to ride but showed incredible self stability when released riderless. This lead Jones to look more closely at front fork geometry and how it affects stability. He theorized that the when the bicycle rolls the steering angle adjusts to minimize the potential energy of the fork/front wheel assembly. So he iteratively calculated the height change of a point on the fork as a function of steer angle and roll angle. From this he determined that the theory wasn't correct because the steer angle never adjusts to the minimal potential energy angle in normal riding conditions.

Jones then realized that the change in height of the point on the fork with respect to the steering angle was proportional to the torque about the steer axis for small steering angles. This led to calculating the constant of proportionality associated with this relationship. This constant was used as his stability index and turned out to simply be the mechanical trail divided by two times the front wheel diameter as shown in [5b] on page 290. Jones used this stability index to make a plot that compared various bicycles. All of the bicycles he found had a negative stability index and most of the modern bicycles were grouped fairly close together.

Using this information Jones made his next bicycle that had a frame geometry which gave a positive stability index. This bicycle had negative trail. It was rideable, although difficult, and fell instantly when released riderless. These three bicycles experimentally verified Jones' self stability index.

This study essentially gave a way to classify, in terms of self stability, bicycles based on their frame geometry. The stability index can then be used as a design tool to allow a new bicycle design to have the same stability characteristics as a previously designed bicycle.

4p) Vincenti, W. G. (1988). How Did It Become 'Obvious' That an Airplane Should Be Inherently Stable? Invention & Technology: 50-56.

This is a great piece that presents a timeline of how the aeronautical community came to understand handling qualities and the balance between stability and control.

5p) Schwab, A. L., J. P. Meijaard, et al. (2004). Benchmark Results on the Linearized Equations of Motion of an Uncontrolled Bicycle. The Second Asian Conference on Multibody Dynamics. Seoul, Korea, KSME.

6p) Limebeer, D. J. N. and R. S. Sharp (2006). Bicycles, Motorcycles, and Models. IEEE Control Systems Magazine. 26: 34-61.