The preventive warning systems are seen as an alternative to rider assistance and risk reduction for Powered Two Wheeled (PTW) vehicles. In this work we propose an analysis of the critical lean dynamics of motorcycle based on a model of double inverted pendulum (DIP). The choice of this structure is motivated by its simplicity and that the model contains the main parts which contribute principally in the PTW vehicle tilt dynamics. The analysis will be focused on the effect of the tire-road adhesion, the longitudinal speed and its dynamics, the road curvature, the road bank angle and the tilt of the rider's upper body.