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Chapters 1 through 5 are essentially a mechanics primer and will start off by reviewing basic concepts and progress by gradually building on these concepts addressing the more challenging aspects of rigid body dynamics. The aim here is to give you enough of a refresher course in mechanics that you can move on to more advanced reading where these fundamentals are prerequisite. If you are already up to speed on the subject of mechanics, you might want to skip direcdy to Chapter 6.
Chapter 1, Basic Concepts
This warm-up chapter covers the most basic of principles that are used and referred to throughout this book. The specific topics addressed include mass and center of mass, Newton’s laws, inertia, units and measures, and vectors.
Chapter 2, Kinematics
This chapter covers such topics as linear and angular velocity, acceleration, momentum, and the general motion of particles and rigid bodies in two and three dimensions.
* A rigid body is formally defined as a body, composed of a system of particles, whose particles remain at fixed distances from each ocher with no relative translation or rotation among particles. Although the subject of mechanics deals with flexible bodies and even fluids such as water, we’ll focus our attention on bodies chat are rigid,
t John Nagle is the developer of Falling Bodies, a dynamics plug-in for Softimage 3D. You can check out his patented technology at www.animats.com.
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Chapter 3, Force
The principles of force and torque are covered in this chapter, which serves as a bridge from the subject of kinematics to that of kinetics. General categories of forces are discussed, including drag forces, force fields, and pressure.
Chapter 4, Kinetics
This chapter combines elements of Chapters 2 and 3 to address the subject of kinetics and explains the difference between kinematics and kinetics. Further discussion treats the kinetics of particles and rigid bodies in two and three dimensions. Chapter 5, Collisions
In this chapter I cover particle and rigid body collision response, that is, what happens after two objects run in to each other.
Chapters 6 through 10 tilje a look at some real-world problems. These chapters focus on modeling with the aim of arming you with a solid understanding of the nature of certain physical systems, specifically the forces involved, such that these systems can be accurately modeled in real-time simulators if you choose to pursue that subject further. The example topics in this part are not meant to be all-inclusive of every system you might try to model in a game. Rather, they were selected to best illustrate the specific physical phenomenon and concepts that are relevant to a wide variety of problems.
Chapter 6, Projectiles
Chapter 6 is the first in a series of chapters addressing specific problems that can be modeled in a game to provide physically realistic content. This first chapter addresses the subject of projectiles and discusses the forces acting on projectiles in flight as well as factors that influence speed and trajectory Chapter 7, Aircraft
This chapter focuses on the elements of flight, including propulsor forces, drag, geometry, mass, and, most important, lift. It also serves as the starting point for a working 3D real-time simulation that will be developed in Chapter 15.
Chapter 8, Ships
The fundamental elements of floating vehicles are discussed in this chapter, including floatation, stability, volume, drag, and speed.
Chapter 9, Hovercraft
Hovercraft have some of the characteristics of both aircraft and boats. This chapter considers the characteristics that distinguish the hovercraft as a unique vehicle. Topics covered include hovering flight, aerostatic lift, and directional control. Chapter 10, Cars
In this chapter, specific aspects of automobile performance are addressed, including aerodynamic drag, rolling resistance, skidding distance, and roadway banking.
Chapters 11 through 17, along with the three appendices, offer an introduction to realtime simulations. These chapters introduce the subject of real-time simulations and discuss various aspects of this field as applicable to computer games. The subject of real-time simulators is vast and deserves an entire book on its own, so this book focuses
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on the fundamentals. I walk you through the development of a 2D simulation of a
couple of hovercraft, a 3D flight simulation, a generic multibody simulation in 3D with
collision response, and a simulation of cloth using particles and springs.
Chapter II, Real-Time Simulations
This chapter introduces the subject of real-time simulations and covers several numerical integration methods for solving the differential equations of motion.
Chapter 12, 2D Rigid Body Simulator
This chapter addresses the practical aspects of implementing a simple 2D particle and rigid body simulator. A simple real-time simulation of a couple of hovercraft is developed in this chapter.
Chapter 13, Implementing Collision Response