Collisions - Physics for Game Programmers - page 160

The frictional impulse acts in the direction normal to the line of action and will change the
velocity components, v n , normal to the line of action.

ˆ F

( )

Fmvv =−

(6.33)

n 1 n 0

In Equation (6.33), v n 0 is the pre-collision normal to the line of action, and v n 1 is the normal
velocity after the frictional impulse has been applied.
In the first part of the topic, it was emphasized that the velocity components normal to the
line of action were unchanged by a collision. This statement is only true for frictionless collisions.
If two objects undergo an oblique collision in which friction is involved, the resulting frictional
impulse will change the velocity components normal to the line of action. In addition, the frictional
impulse will also cause the objects to spin, a subject that will be explored in the next section.

Modeling Two-Dimensional Oblique Collisions
Now that the concept of a frictional impulse has been introduced, we are ready to tackle the
problem of modeling a general two-dimensional oblique collision. We will start by looking at a
simplified problem, shown in Figure 6-14, of an object striking the face of a ramp that is inclined
at an angle of q . The line of impact of the collision is shown by the dotted line. When the object
strikes the ramp, it is traveling at a velocity, v , which can be split into components along the
line of action, v p 0 , and normal to the line of action, v n 0 .

v n0

v p0

v

θ

Figure 6-14. A general, two-dimensional oblique collision

When the object collides with the ramp, it has a velocity component, v n 0 , parallel to the
face of the ramp, so the object begins to slide up the ramp. The frictional impulse generated by
the collision resists the sliding motion and reduces the magnitude of v n 0 to a new value, v n 1 ,
according to Equation (6.33). As shown in Figure 6-15, the frictional impulse causes an angular
impulse that causes the object to rotate with an angular velocity, w . Also shown in Figure 6-15
are the rotated coordinate axes in the p and n directions.