Motorcycle lateral and longitudinal dynamic modeling in presence of tyre slip and rear traction

This paper proposes a mathematical model of a motorcycle that deals with the lateral and longitudinal dynamics, the tyre slip and the rear wheel traction. The vehicle is considered as an assembly of two rigid bodies. The proposed dynamic formulation is based on Lagrange's equations, it allows to formulate the equations of motion with 7 degrees of freedom (DoF). The model assess the vehicle behavior in response to a propulsion torque applied to the rear wheel and a rider torque applied to the motorcycle handlebar. The model is able to describe the coupling of the in-plane (longitudinal) and out-of-plane (lateral) dynamics taking into account the rear and the front longitudinal tyre slip related to the rear wheel traction. In order to solve the linearized equations of motion, no multibody software was used, only numeric simulation tools such as MATLAB.