Game Development Reference
In-Depth Information
CHAPTER 2
Kinematics
In this chapter we'll explain the fundamental aspects of the subject of kinematics.
Specifically, we'll explain the concepts of linear and angular displacement, velocity, and
acceleration. We've prepared an example program for this chapter that shows you how
to implement the kinematic equations for particle motion. After discussing particle
motion, we go on to explain the specific aspects of rigid-body motion. This chapter,
along with the next chapter on force, is prerequisite to understanding the subject of
kinetics, which you'll study in Chapter 4 .
In the preface, we told you that kinematics is the study of the motion of bodies without
regard to the forces acting on the body. Therefore, in kinematics, attention is focused
on position, velocity, and acceleration of a body, how these properties are related, and
how they change over time.
Here you'll look at two types of bodies, particles and rigid bodies. A rigid body is a
system of particles that remain at fixed distances from one another with no relative
translation or rotation among them. In other words, a rigid body does not change its
shape as it moves—or any changes in its shape are so small or unimportant that they
can safely be neglected. When you are considering a rigid body, its dimensions and
orientation are important, and you must account for both the body's linear motion and
its angular motion.
A particle, on the other hand, is a body that has mass but whose dimensions are negli‐
gible or unimportant in the problem being investigated. For example, when considering
the path of a projectile or a rocket over a great distance, you can safely ignore the body's
dimensions when analyzing its trajectory. When you are considering a particle, its linear
motion is important, but the angular motion of the particle itself is not. Think of it this
way: when looking at a particle, you are zooming way out to view the big picture, so to
speak, as opposed to zooming in as you do when looking at the rotation of rigid bodies.