Game Physics [With CDROM] (Hardcover, 2)

Introduction
A Brief History of the World
A Summary of the Topics
Examples and Exercises
Basic Concepts from Physics
Rigid Body Classification
Rigid Body Kinematics
Newton’s Laws
Forces
Momenta
Energy
Rigid Body Motion
Newtonian Dynamics
Lagrangian Dynamics
Euler’s Equations of Motion
Deformable Bodies
Elasticity, Stress, and Strain
Mass?Spring Systems
Control Point Deformation
Free-Form Deformation
Implicit Surface Deformation
Fluids and Gases
Vector Calculus
Strain and Stress
Conservation Laws
A Simplified Model for Fluid Flow
Implementing the Simplified 2D Model
Implementing the Simplified 3D Model
Variations of the Simplified Model
Physics Engines
The Physics Tick
Collision Culling
Test-Intersection Queries
Collision Detection with Convex Polyhedra
Unconstrained Motion
Acceleration-Based Constrained Motion
Velocity-Based Constrained Motion
Variations
Linear Algebra
A Review of Number Systems
Systems of Linear Equations
Matrices
Vector Spaces
Advanced Topics
Affine Algebra
Introduction
Coordinate Systems
Subspaces
Transformations
Barycentric Coordinates
Calculus
Univariate Calculus
Multivariate Calculus
Applications
Quaternions
Rotation Matrices
The Classical Approach
A Linear Algebraic Approach
Interpolation of Quaternions
Derivatives of Time-Varying Quaternions
Differential Equations
First-Order Equations
Existence, Uniqueness, and Continuous Dependence
Second-Order Equations
General-Order Differential Equations
Systems of Linear Differential Equations
Equilibria and Stability
Ordinary Difference Equations
Definitions
Linear Equations
Constant Coefficient Equations
Systems of Equations
Numerical Methods
Euler’s Method
Higher-Order Taylor Methods
Methods via an Integral Formulation
Runge?Kutta Methods
Multistep Methods
Predictor?Corrector Methods
Extrapolation Methods
Verlet Integration
Numerical Stability and Its Relationship to Physical Stability
Stiff Equations
Linear Complementarity and Mathematical Programming
Linear Programming
The Linear Complementarity Problem
Mathematical Programming
Applications
Contact Forces