© Kluwer (second edition, 1999).
Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors. Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It contains sufficient material for a course on mathematical topics alone.
The second edition has been expanded by nearly a hundred pages on relativistic mechanics. The treatment is unique in its exclusive use of geometric algebra and in its detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.
Chapter 1: Origins of Geometric Algebra
1-1. Geometry as Physics
1-2. Numbers 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 Identites and Definitions
2-2. The Algebra of a Euclidean Plane
2-3. The Algebra of a 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 Resistence
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 Symmetric Top
7-4. Integrable Cases of Rotational Motion
7-5. Rolling Motion
7-6. Implusive 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 Representaions
9-2. Spacetime Maps and Measurements
9-3. Relativistic Particle Dynamics
9-4. Energy-Momentum Conservation
9-5. Relativistic Rigid Body Mechanics
Appendices
A. Spherical Trigonometry
B. Elliptic Functions
C. Units, Constants and Data
Errata for Chapter 9 on Relativity
Errata for Chapter 9
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