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.