Jordan Forms in Vehicle Dynamics

— In the ongoing search for mathematically efficient methods of predicting the motion of vehicle and other multibody systems, and presenting the associated results, one of the avenues of continued interest is the linearization of the equations of motion. While linearization can potentially result in reduced fidelity in the model, the benefits in computational speed often make it the pragmatic choice. When representing the governing equations of any linear system, one of the relevant problems is the determination of the mathematically equivalent formulation of the smallest size, and solving this system is the most mathematically efficient manner. This paper discusses and explores the potential of an approach based on modal identification, and the Jordan form of the system matrix. The paper includes an example where the method is applied to the classic linear bicycle model.