[内容简介]This book provides an introduction to geometric algebra as an unified language for physics and mathematics. It containes extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition.Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces new, coordinatefree methods for rotational dynamics and orbital mechanics,developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in governmental and industrial space programs, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion.
[目次]Chapter 1: Origins of Geometric Algebra
1-1.Geometry as Physics
1-2.Number and Magnitude
1-3.Directed Numbers
1-4.The Inner Product
1-5.The Outer Product
1-6.Synthesis and Simplification
1-7.Axioms for Geometric Algebra
Chapter 2: Developments in Geometric Algebra
2-1.Basic Identities and Definitions
2-2.The Algebra of a Euclidean Plane
2-3.The Algebra of Euclidean 3-Space
2-4.Directions, Projections and Angles
2-5.The Exponential Function
2-6.Analytic Geometry
2-7.Functions of a Scalar Variable
2-8.Directional Derivatives and Line Integrals
Chapter 3: Mechanics of a Single Particle
3-1.Newton's Program
3-2.Constant Force
3-3.Constant Force with Linear Drag
3-4.Constant Force with Quadratic Drag
3-5.Fluid Resistance
3-6.Constant Magnetic Field
3-7.Uniform Electric and Magnetic Fields
3-8.Linear Binding Force
3-9.Forced Oscillations
3-10.Conservative Forces and Constraints
Chapter 4: Central Forces and Two-Particle Systems
4-1.Angular Momentum
4-2.Dynamics from Kinematics
4-3.The Kepler Problem
4-4.The Orbit in Time
4-5.Conservative Central Forces
4-6.Two-particle Systems
4-7.Elastic Collisions
4-8.Scattering Cross Sections
Chapter 5: Operators and Transformations
5-1.Linear Operators and Matrices
5-2.Symmetric and Skewsymmetric Operators
5-3.The Arithmetic of Reflections and Rotations
5-4.Transformation Groups
5-5.Rigid Motions and Frames of Reference
5-6.Motion in Rotating Systems
Chapter 6: Many-Particle Systems
6-1.General Properties of Many-Particle Systems
6-2.The Method of Lagrange
6-3.Coupled Oscillations and Waves
6-4.Theory of Small Oscillations
6-5.The Newtonian Many Body Problem
Chapter 7: Rigid Body Mechanics
7-1.Rigid Body Modeling
7-2.Rigid Body Structure
7-3.The Symmetrical Top
7-4.Integrable Cases of Rotational Motion
7-5.Rolling Motion
7-6.Impulsive Motion
Chapter 8: Celestial Mechanics
8-1.Gravitational Forces, Fields and Torques
8-2.Perturbations of Kepler Motion
8-3.Perturbations in the Solar System
8-4.Spinor Mechanics and Perturbation Theory
Chapter 9: Relativistic Mechanics
　9-1.Spacetime and Its Representations
　9-2.Spacetime Maps and Measurements
　9-3.Relativistic Particle Dynamics
　9-4.Energy-Momentum Conservation
　9-5.Relativistic Rigid Body Mechanics
Appendix
　A Spherical Trigonometry
　B Elliptic Functions
　C Units, Constants and Data
Hints and Solutions for Selected Exercises
References
Index