Bicycle cornering dynamics

In the first stage, the bike needs to correct its leaning (roll-axis) to approach corner. This is achieved by counter-steer. At this moment, the front wheel has larger 'slip angle' than the rear; or in another word, the front wheel experiences more lateral force (friction) than the rear.

The figure below describes the forces and torque that acts on the bike, with the frame of reference at the centre of combined mass (rider and bike).

Figure 1: Forces (blue) and Torque(red) acting on the bike in the 'counter-steering' step. Left image is top-bottom view, right image is rear-front view of the bicycle. Front wheel create lateral force (friction) that both 'yaw' and 'roll' the bike.

Once the bike starts to roll (counter-clockwise as in Figure 1), rider starts to steer into the direction that they would like to go. The action once again create extra lateral force (friction) on the front tyre, which would create torque in roll-axis (clock-wise, to stop the bike from dropping) and to 'yaw' the bike to the direction rider wish to follow. At first, the front experiences more side-way friction than the rear. However, the rear and the front tyre will create equal lateral force (friction), to 1) stop the bike from rolling (roll-axis), and 2) creating centripetal force that is required for the cornering.

Figure 2: Forces (blue) and Torque(red) acting on the bike at the first step of steering. Left image is top-bottom view, right image is rear-front view of the bicycle.