1978
Using 78
Gobas, a technique which he calls the Boltzmm Hamel method, in 1978 Gobas presented a linearized set of equations very similar in form to Neymark and Fufaev
I -
[1967]. Gobas equations, (1.4) in his paper, incorporate the forward acceleration of
the bicycle, V , Setting V terms to zero and comparing, we think the lean equation may be correct, but in the steer equation the coefficient to the
xr term seems to be
in disagreement with the equations in our Chapter 1 1 The variable b is not d e h e d 1.
in the paper but we suspect that it is equivalent to our v .
Gobas refers to NeYmark and Fufaev, but does not compare equations.
Adiele, 1979
In his 1979 Masters thesis Adiele, who w s focusing on design optimization a
and performance evaluation of two-wheeled vehicles, derived nonlinear equations of
motion for the Basic bicycle with tire side slip using Kanes method of generalized active and inertia forces. His equations, representing lateral motion, lean, steer, and yaw (in that order) are present in matrix form on pages 22-24 of his thesis. His variable V is
OUT
Xr,
X is our
xr, is our +, and r 6
is our 8. Because his equations resembled Sharps ,
El9711 four equations, we expanded Adieles matrix, linearized his equations for
small values of X and 8, and compared them to the equations in Sharps [1971]
Appendix I. The results show that Adieles equations are in error, missing several terms
79 compared to Sharp and having severd sign errors. However, by allowing front
mass the to be zero his equations are nearly correct.
Adiele refers to Roland [1971], but does not compare equations. A subsequently published paper by Taylor and Adiele [1980] on stability in large angle steady turns
1 -
also appears to rely on Adiele's equations, even though the authors evidently knew
of earlier linearized studies (by Weir, and others) which they could have used to
check their equations.
Lowell and Mckell, 1982
In 1982 Lowell and Mckell, using ad hoc arguments similar in style to Pearsall
[1922] derive a set of linearized equations for a Basic bicycle model with a point mass
in the rear part, some steering inertia aad front gyroscopic effects, but no front mass,
m d no tilt of the steering axis. When compared to our equations simplified for this
case, we find there is significant disagreement. Several terms have been neglected in both the lean and steer eq...