Game Development Reference
In-Depth Information
CHAPTER 4
Kinetics
Recall that kinetics is the study of the motion of bodies, including the forces that act on
them. It's now time that we combine the material presented in the earlier chapters—
namely, kinematics and forces—to study the subject of kinetics. As in Chapter 2 on
kinematics, we'll first discuss particle kinetics and then go on to discuss rigid-body
kinetics.
In kinetics, the most important equation that you must consider is Newton's second law:
F = m a
When rigid bodies are involved, you must also consider that the forces acting on the
body will tend to cause rotation of the body in addition to translation. The basic rela‐
tionship here is:
M cg = I α
where M cg is the vector sum of all moments (torques) acting on the body, I is the body
moment of inertia tensor, and α is the angular acceleration.
Collectively, these two equations are referred to as the equations of motion .
There are two types of problems that you will encounter in kinetics. One type is where
you know the force(s) acting on the body, or you can estimate them, and you must solve
for the resulting acceleration of the body (and subsequently its velocity and displace‐
ment). Another type is where you know the body's acceleration, or can readily determine
it using kinematics, and you must solve for the force(s) acting on the body.