A bicycle model for education in multibody dynamics and real-time interactive simulation

This paper describes the use of a bicycle model to teach multibody dynamics. The bicycle motion equations are first obtained as a DAE system written in terms of dependent coordinates that are subject to holonomic and non-holonomic constraints. The equations are obtained using symbolic computation. The DAE system is transformed to an ODE system written in terms of a minimum set of independent coordinates using the generalised coordinates partitioning method. This step is taken using numerical computation. The ODE system is then numerically linearised around the upright position and eigenvalue analysis of the resulting system is performed. The frequencies and modes of the bicycle are obtained as a function of the forward velocity which is used as continuation parameter. The resulting frequencies and modes are compared with experimental results. Finally, the non-linear equations of the bicycle are used to create an interactive real-time simulator using Matlab-Simulink. A series of issues on controlling the bicycle are discussed. The entire paper is focussed on teaching engineering students the practical application of analytical and computational mechanics using a model that being simple is familiar and attractive to them.