G.R.R. Routh, 'On the motion of a bicycle',  The Messenger of Mathematics, 
vol. 28, May 1898 - April 1899, pp. 151-169. 

In four sections, four problems are considered. They all deal with the case 
with prescribed small steer input and zero trail. In this case the wheelbase 
can be considered to be constant. Except in the first problem, only the rear 
frame has mass, as in Boussinesq's model. There are quite a few small 
errors. 

I. Bicycle with locked steer. The unstable falling motion is independent of 
the forward speed. 

II. Small oscillations about a steady motion in a straight line. The steer 
angle is assumed to be proportional to the lean angle, which can stabilize the 
bicycle. 

III. Steady circular motion. Also the lateral forces at the tires are 
considered. 

IV. Stability of the steady circular motion. For wide curves, the conditions 
are essentially the same for the motion in a straight line. 

List of errors.

page 152, line 9: apparently d^2 z/dt^2 is meant instead of dv/dt 
page 152, line 6 from below: A^2 should read a^2

page 153, line 2: A_2^2 should read a_2^2

page 157, line 10 from below: p' should read p (no prime)

page 159, line 6: factor 1/2 for the real root is missing 

page 160, line 2: prime at omega_1 is missing
page 160, line 4: prime at omega_3 is missing; sin(beta) should be sin(p) 
page 160, line 5: final cos(beta) should be cos(p) 
page 160, line 7: minus before last term should be plus 
page 160, line 14: last cos(p) should be sin(p) 
page 160, passim and following pages: Omega_3 should be omega_3, or at least 
                                      they are always equal. 

page 161, eq. (8): minus sign missing before h

page 163, last line: l_3 should be l_2; 
                     R_1 in the second equation should be R_2

page 164, line 4: factor omega^2 missing; this is also the case in the two 
                  corresponding expressions lower on the same page. 

page 165, line 9 from below: factor sin(beta) missing in the first term. 
page 165, line 3 from below: factor cos(p_0) missing in the last term; 
                             this error propagates over the following pages:
                             second terms of eq. (10) and (14) on page 166 
                             and line 6 of page 167; also in last term of 
                             line 10 of page 167.

page 166, eq. (14), second term: transpose beta and sin 

JPM, Nottingham, 12 September 2007.