Game Development Reference
In-Depth Information
CHAPTER 4
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Basic Kinematics
T
he previous chapter introduced Newtonian mechanics and the subjects of force, work, energy,
and power. We encountered Newton's three laws of motion, which characterize the behavior
of forces and relate a force applied to an object to the resulting acceleration of the object. In
this chapter, we will expand the discussion of Newton's laws of motion to explore the field of
kinematics—the study of motion. This chapter will provide you with the basic models and
equations that govern the motion of all objects.
Understanding the laws of motion is critically important to game programming. Pretty
much every live-action game will involve things flying through the air, driving along the ground,
moving through water, and so on. A good understanding of kinematics will give your games
realism. You will apply the concepts you learn in this chapter to just about every live-action
game you will program.
To cover the subject of basic kinematics, this chapter will explore the following topics:
•
The equations that govern acceleration, velocity, and location in translational motion
•
Solving the translational equations of motion
•
The equations that govern rotational motion
•
The concepts of torque, moment of inertia, and center of mass
•
Rigid body motion
Translational Motion
The first topic this chapter covers is the development of the equations that describe the linear,
or translational, motion of an object. Translational motion describes the movement of an
object through space. You will have to model translational motion all the time in your game
programming—modeling the flight of a golf ball, simulating an airplane flying through the air,
or modeling a car driving around a curve are just a few of the many types of translational
motion that a game programmer might have to simulate.
The mathematical description of translational motion begins with Newton's second law,
F = ma
. Once the net external forces on an object have been evaluated, the acceleration of the
object can be determined. Knowing the acceleration allows the determination of the velocity
and location of the object at any point in time. Let's start our discussion of translational motion
by talking about the relationship between force, acceleration, velocity, and location.
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