C. Bourlet, 

Etude theorique sur la bicyclette

Bulletin de la Societe Mathematique de France 27 (1899), pp. 47-67, 76-96. 

(available from Numdam, http://www.numdam.org)

Not much remains to be discussed here. There is the geometric issue of 
assumed constant wheelbase and zero pitch angle. The steer angle is initially 
taken into account, but on simplifying the equations on page 65, it is 
assumed that the inclination angles of the rear and front wheels are the same, 
which is only true for small angles if the steer axis is vertical. In the 
first equation on page 65, the gyroscopic term coming from the last term 
in equation (27), page 63, a linear contribution, is for some reason not 
taken into account. If this term is included in the equation on page 65, and 
the equations are linearized, the correct lean equation is obtained 
(with the further assumptions of zero mass of the handle bar/front fork 
and zero trail). 

In general, the conditions for slipping of the tyres are only approximately 
valid. Compare with the slightly more general treatment by Routh. 

It seems that this is one of the first publications in which the 
'Cornu spiral' (clothoid) is mentioned for the shape of a bend. 

Further remarks:

page 51: 'dextrorsum': apparently, this is what we call now left-handed. 

page 55: 'forces centrifuges composees': that are what we call now Coriolis 
     forces. 

page 63, eq. (27): the first E' should be F' 
     (compare with equation on page 65). 

page 92, eq. (43): the final cos(psi) should be sin(psi) 
     (compare with eq. (42) and eq. (42 bis)). 

JPM, Nottingham, 12 September 2007