THE BENCHMARKED LINEARIZED EQUATIONS OF MOTION FOR AN IDEALIZED BICYCLE (IMPLEMENTED IN SOFTWARE AND DISTRIBUTED VIA THE INTERNET)

Abstract

People have been successfully building and riding bicycles since the 1800s, and many attempts have been made to describe the motion of these machines mathematically. However, common acceptance of the correct linearized equations of motion for a bicycle has remained elusive. In his 1988 master?s thesis at Cornell University, Scott Hand derived the equations again and performed the first known extensive survey of the literature, finding and documenting the mistakes made in previous attempts. The question remained however of what mistakes, if any, Mr. Hand and his advisors made. The subsequent advent of cheap and plentiful computing power and the development of numerical methods to take advantage of it provide an opportunity to confirm, once and for all, the correct linearized equations of motion for an idealized bicycle. That is exactly what A. L. Schwab, J. P. Meijaard, and J. M. Papadopoulos have done in their recent paper. The next step is to efficiently promulgate these correct and confirmed equations in a useful form. The goal is that anyone working in the areas of bicycle or motorcycle handling or control can use these equations directly or verify their own underlying equations against this benchmark. This thesis describes a program, JBike6, its on-line help, and its web site designed specifically for that purpose: to provide a turn-key application for evaluating the self-stability of a bicycle. JBike6 also generates numbers (eigenvalues and matrix entries) that can be used to compare, to very high precision, against any other linearized or fully non-linear equations of motion for a bicycle. After a brief review of the application, theory, and results of JBike6, the contents of this thesis consist primarily of hard copy of the on-line help and web site and screen shots of the program. The text has been modified to be more readable as a narrative and some pictures have been formatted to fit within the margins. Obviously, the interactive nature of the program, the help file, and the web site, including the hyperlinks, animations, and videos, is not available in this printed document. While all the components will continue to evolve, this thesis is a snapshot of them in September 2006. Many redundancies have been removed, but some remain in order to preserve the integrity and flow of the individual components. All these components may currently be found on-line at www.tam.cornell.edu/~ad29/JBike6