Geometry

In their most basic form and for the sake of the simple physics I will apply to these vehicles, motorcycles are composed of a frame, two wheels and tires, and handlebars for steering. There are a lot more parts and factors that make a motorcycle move but the physics involved can be described more easily by simplifying the system in this way.

Geometry of a Motorcycle
(Cossalter pg 4)

Geometry

This image makes it apparent that even with a simplified system there are still a lot of things having an effect on the success of the vehicle. The wheelbase and trail are particularly important as far as handling is concerned and are also two things that are commonly changed when customizing motorcycles. A long wheel base will make the ride smoother and more comfortable in a straight line but will also diminish close handling capabilities. Alteration of the caster angle, or the angle at which the forks sit, has an effect on the handling of the motorcycle as well. An increase in the caster angle, much like in wheelbase, creates better straight line stability but decreases cornering capabilities (Cossalter).

Another important geometric feature that effects the handling of the motorcycle is the trail. The trail is measured by the intersection of the ground and the projection of where the forks (if they were extended) hit the ground.

Positive trail diagram
(Cossalter pg 6)

Often motorcycles are customized in such ways that the trail is altered. These alterations cause significant changes to the handling of the vehicle. Due to the way the tire interacts with the road making the value of the trail negative causes the friction on the tire to push direction of the wheel out of equilibrium, and therefore the vehicle will no longer travel in a straight line on its own. This is also a problem when uneven road surfaces are encountered. The change in terrain under the tire temporarily changes the trail causing forces to interact with the tires differently (Cossalter).