This paper presents a motorcycle direct dynamic formulation by the Jourdain's principle approach. This vehicle is considered as an assembly of six rigid bodies and the resulting equation of motion allows to simulate 11 degrees of freedom. The vehicle geometry is described and a step-by-step procedure is introduced to evaluate the kinematics and the generalised efforts of the considered vehicle. In addition, to simulate the equation of motion, a Lyapunov-based stabilisation is developed to assess the vehicle behaviour in response to a propulsion/braking torque applied on the vehicle's wheels and a rider torque exerted on the motorcycle's handlebar. Simulation results reveal some dynamic features such as load transfer and counter-steering phenomena.