Game Development Reference

In-Depth Information

what each particle making up the rigid body is doing all the time. Thus, you treat the

rigid body's linear motion and its angular motion separately. When you do need to take

a close look at specific particles of—or points on—the rigid body, you can do so by taking

the motion of the rigid body as a particle and then adding to it the relative motion of

the point under consideration.

Figure 2-12
shows a rigid body that is traveling at a speed
v
cg
, where
v
cg
is the speed of

the rigid body's center of mass (or center of gravity). Remember, the center of mass is

the point to track when treating a rigid body as a particle. This rigid body is also rotating

with an angular velocity
ω
about an axis that passes through the body's center of mass.

The vector
r
is the vector from the rigid body's center of mass to the particular point of

interest,
P
, located on the rigid body.

Figure 2-12. Relative velocity

In this case, we can find the resultant velocity of the point,
P
, by taking the vector sum

of the velocity of the body's center of mass and the tangential velocity of point
P
due to

the body's angular velocity
ω
. Here's what the vector equation looks like:

v
R
=
v
cg
+
v
t

or:

v
R
=
v
cg
+ (
ω
×
r
)

You can do the same thing with acceleration to determine point
P
's resultant accelera‐

tion. Here you'll take the vector sum of the acceleration of the rigid body's center of