ABSTRACT
ABSTRACT: The application of a frozen-time eigenvalue analysis to the straight line accelerating and braking of a race-car is presented. A three degree-of-freedom, single-track vehicle model is used to derive linear time-varying equations of motion. The response of the time-varying system is correlated with the frozen-time eigenvalues to predict the system stability. Theoretically, the use of eigenvalues to determine the stability of a time-varying system is only valid if the system is changing ‘sufficiently slowly’. Bounds on the rate-of-change of the time-varying system are derived to determine the conditions under which this analysis is valid. Numerical evaluation of these bounds shows that the model studied can be classified as slowly-varying under accelerating and braking conditions, and is stable when the frozen-time eigenvalues are negative.
