Game Development Reference
e = −(v 1+ − v 2+ ) / (v 1− − v 2− )
Here e is known as the coefficient of restitution and is a function of the colliding objects'
material, construction, and geometry. This coefficient can be experimentally deter‐
mined for specific impact scenarios—for example, the collision between a baseball and
bat, or a golf club and ball. For perfectly inelastic collisions, e is 0, and for perfectly elastic
collisions, e is 1. For collisions that are neither perfectly inelastic nor perfectly elastic, e
can be any value between 0 and 1. In this regard, the velocities considered are along the
line of action of the collision.
In frictionless collisions, the line of action of impact is a line perpendicular (or normal)
to the colliding surfaces. When the velocity of the bodies is along the line of action, the
impact is said to be direct . When the line of action passes through the center of mass of
the bodies, the collision is said to be central . Particles and spheres of uniform mass
distribution always experience central impact. Direct central impact occurs when the
line of action passes through the centers of mass of the colliding bodies and their velocity
is along the line of action. When the velocities of the bodies are not along the line of
action, the impact is said to be oblique . You can analyze oblique impacts in terms of
component coordinates where the component parallel to the line of action experiences
the impact, but the component perpendicular to the line of action does not. Figure 5-1
illustrates these impacts.
Figure 5-1. Types of impact
As an example, consider the collision between two billiard balls illustrated in Figure 5-2 .