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### Adiele1979Hand88

Course: ALS 93, Fall 2009
School: Cornell
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Word Count: 500

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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...

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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...

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Cornell - ALS - 93
77inertia are assumed to be parallel and perpendicular to the steering a x i s equationsof motion. Other than this, these equations are equivalent to those in Sharps 1971paper, which when simplified correctly formed a subset of the equations pres
Cornell - ALS - 93
63correct for the rear part of his simplified model, but not for the front unless trail vanishes. Also, (b) he has left out the lateral offset of the front and rear mass center from the track Line due to steer angle; this too is correct for the rear
Cornell - ALS - 93
62Bower, 1915Bower in 1915, without reference to any previous bicycle work, derived the linearized equations of motion for a simplified Basic bicycle model at the end of an1 -article mainly concerning the gyroscopic effects of the engine and w
Cornell - ALS - 93
Journalof Sound and Vibration(1988) 126(3), 545-549LETTERSIN-PLANE VIBRATIONTO THEEDITORRECTANGULAR PLATESOF POINT-SUPPORTEDThe natural frequencies (the dimensionless frequency parameters) and the mode shapes of in-plane vibration are
Cornell - ALS - 93
65offset from the steering axis. When linearized, we find this lean equation agrees with our lean equation simplified for an equivalent configuration.D ohring, 1955In 1955, in order to more generally analyze the stability of motorcycles andmotor
Cornell - ALS - 93
76Besides stating that comparing his equations agree with to Sharps, Weir refersto Whipple [1899], Pearsall [1922], Dijhring [1955], Singh [1964], Singh and Goel[1971], but does not compare his equations to these works.;-Singh and Goel, 197
Cornell - ALS - 93
69Nez'mark and Fufaev, 1967tIn 1967 Nelimark and Fufaev (N &amp; F) with a brief reference to Dijhring [1955] derived equations of motion of the bicycle as a classical example of a nonholonomic-system. In their derivation they use Lagrange's equ
Cornell - ALS - 93
Cornell - ALS - 93
75Roland refers to the works of Whipple [1899], Bower [1915], Pearsall [1922],Manning [1951],Dijhring [1955], Collins [1963], Singh [1964],and also Singh andGoel [19?1]. However, he makes no comparisons to their equations of motion.I-Weir,
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