The behavior of motorcycles during rectilinear motion depends on the longitudinal forces exchanged between the tires and the road, the aerodynamic forces originating during this motion, and the slope of the road plane. The study of rectilinear motion highlights certain dynamic aspects that are also important for safety, such as the motorcycle's behavior during braking with a possible forward overturning, and in acceleration, with possible wheeling.

During steady turning motion the motorcycle can have neutral, under or oversteering behavior. To maintain equilibrium the rider applies a torque to the handlebars that can be zero, positive, in the same direction of the handlebar rotation, or negative, i.e., applied in the direction opposite to the rotation of the handlebar. These characteristics are important and concur to define the sensation of the motorcycle's handling.

A motorcycle without suspension moving over irregular ground presents difficulties in steering because of the loss of wheel grip on the road plane, and because of rider discomfort. Small bumps on the ground are easily absorbed by the tires, but for adequate absorption of larger bumps, the motorcycle needs appropriate suspension.
A motorcycle with suspension, from a dynamics point of view, can be considered as a rigid body connected to the wheels with elastic systems (front and rear suspension). The rigid body constitutes the sprung mass (chassis, engine, steering head, rider), while the masses attached to the wheels are called unsprung masses.
Suspension had to satisfy the following three purposes:

• to allow the wheels to follow the profile of the road without transmitting excessive vibration to the rider. This purpose concerns rider comfort, that is the isolation of the sprung mass from the vibration generated by the interaction of the wheels with road irregularities;
• to ensure wheel grip on the road plane in order to transmit the required driving and braking forces;

• to ensure the desired trim of the vehicle under various operating conditions (accelerated motion, braking, entering and leaving turns).
  

The degree of required comfort varies according to the use of the vehicle. For example, in racing vehicles, comfort is less important than the motorcycle's capacity to keep the wheels in contact with the ground and to assume the desired trim. However, in other vehicles the suspension is expected to serve other purposes. For example, in cross-country vehicles the suspension serves to isolate the sprung mass from continuous impact generated by the vehicle jumps. For this reason, suspension in cross-country vehicles has greater wheel travel than in touring vehicles, and more so than in racing vehicles.
As to the trim, it much be stressed that it depends on the stiffness of the suspension. The load can be quite variable in motorcycles (one or two passengers, possibly with baggage); and further, load transfer between the front and rear wheel occurs in both acceleration and braking.

In the previous chapters, the forces operating on the motorcycle were calculated: resistant forces, driving force and dynamic loads on the wheels, in different conditions of both stationary and non stationary motion, in acceleration and in braking. In this chapter, variations in the trim taken by the motorcycle in various driving conditions will be studied instead, and the importance covered by the chain force will be highlighted.
The term vehicle trim implies the geometric configuration that the motorcycle takes in different conditions in steady-unsteady motions, in acceleration and in braking.
As shown below, the motorcycle's trim depends on the stiffness characteristics of the front and rear wheel suspension, on the forces operating on the motorcycle, and on the inclination angle of the chain and the swinging arm. 

As everyone knows, the front and/or rear end of a motorcycle in motion can start to oscillate around the steering axis, especially if the wheels are unbalanced. This phenomenon is easy to observe experimentally, for example by gradually slowing down the motorcycle from a fairly high speed. Oscillations can be observed at certain speed if the front wheel is, statically or dynamically, out of balance. They reach their maximum amplitude and then decrease as speed decreases until they disappear completely. Rear-end oscillations can be observed when traveling over a transversal bump or by exciting the rear frame with an impulsive movement of the trunk. Front end oscillations exhibit their greatest amplitude at a higher speed than rear-end oscillations do. At a low speed it can also be easily observed that the motorcycle tends to fall over sideways, regardless of what the rider does. These experimental observations of motorcycle dynamics who that there are three major modes:

• capsize, a non oscillation mode used and controlled by the rider;
• weave, an oscillation of the entire motorcycle, but mainly the rear end;
• wobble, an oscillation of the front end around the steering axis which does not involve the rear end in any significant way.

In this chapter, firstly we will study these modes using simplified models and later on the in-plane and out of plane modes will be studies by means of an eleven degree of freedom models.

A motorcycle's dynamic properties are described using terms like maneuverability, handling and stability. Maneuverability and handling describe the motorcycle's ability to execute complicated maneuvers, and how difficult it is for the rider to perform them. Stability, on the other hand, means a motorcycle's ability to maintain equilibrium in response to outside disturbances like an uneven road surface or gusts of wind.