Game Development Reference
In-Depth Information
When they collide, the two objects will experience an impulse of force due to the collision.
The magnitude of the impulse will be equal for both objects but will act in opposing directions. The
geometric line along which the impulse acts is called the line of action for the collision. The line
of action of the collision is a line drawn normal, or perpendicular, to the tangential plane at the
point of collision. For the collision of the two spheres shown in Figure 6-4, the line of action is
a line drawn through the center of the spheres that goes through the point of contact.
To develop the equations that determine post-collision velocity, we will consider the colli-
sion of two spheres such that the line of action of the collision is parallel to the x-axis as shown
in Figure 6-4. We will also assume that the impulsive force is significantly greater than all other
forces acting on the colliding objects. For the duration of the collision, all other forces acting on
the objects can be ignored. There is also assumed to be no friction between the two objects.
Figure 6-4. A collision causes an impulse of force to act along the line of action.
The linear impulse of force caused by the collision changes the velocity of the objects. The
post-collision velocity components for the first object can be determined from Equation (6.7).
Since the line of action for the collision is parallel to the x-axis, the linear impulse in the y-
direction is equal to zero.
ˆ x
(
)
=−
Fmv v
(6.10a)
11
x
1
x
0(
=
mv
v
)
(6.10b)
11
y
1
y
In Equation (6.10), the pre-collision velocity components of object 1 are v 1 x and v 1 y , and
the post-collision velocity components are v′ 1 x and v′ 1 y . The collision produces an equal-but-
opposite linear impulse applied to object 2. The post-collision velocities for object 2 can also be
determined from Equation (6.7)
ˆ x
(
)
−=
Fmv v
(6.11a)
22
x
2
x
0
=
mv
(
v
)
(6.11b)
22
y
2
y
ˆ x
Because the same linear impulse, , acts on objects 1 and 2, the right-hand side of
Equations (6.10a) and (6.11a) can be set equal to each other. If this operation is performed and
the two expressions shown in Equations (6.10b) and (6.11b) are simplified, the result is three
equations that define the post-collision velocities of the two objects.
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