Game Development Reference
In-Depth Information
12.4
Impulsive Forces and Collisions
In video games, things are always ramming into each other, so it seems
appropriate for us to spend some time talking about collisions. As we've
mentioned, in the real world, momentum does not change instantaneously;
rather, a large force acts over a very small period of time. However, despite
reality (remember the first law of video game physics), it is frequently the
case that the interval during which these forces act is below the resolution of
our physics time step, and for practical purposes we can consider the change
in momentum to have happened instantaneously. The most important and
common scenario is when the object is involved in a collision. Since the
mass of most objects is constant, an instantaneous change in momentum
usually boils down to an instantaneous change in velocity.
Consider two objects traveling towards each other in one dimension,
with masses m
1
and m
2
and velocities v
1
and v
2
, as illustrated in Fig-
ure 12.9.
V
1
V
2
M
1
M
2
V
'
1
V
'
2
M
1
M
2
Figure 12.9
A collision
Using the momentum relation p = mv, we can calculate the momentum
of the two objects (denoted p
1
and p
2
) and the system as a whole (denoted
as simply p) before and after the collision. We assume that the masses
remain constant and put primes on the symbols that refer to the values
after the collision:
p
1
= m
1
v
1
,
p
2
= m
2
v
2
,
p = p
1
+ p
2
= m
1
v
1
+ m
2
v
2
,
′
′
′
′
′
′
′
′
′
p
1
= m
1
v
1
,
p
2
= m
2
v
2
,
p
= p
1
+ p
2
= m
1
v
1
+ m
2
v
2
.
The change in momentum of each object, according to the law of conser-
vation of momentum, is actually the result of a force acting over time. How-
ever, we think of the collision here as producing an instantaneous change
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