PrefaceChapter 1: Origins of Geometric Algebra1-1.Geometry as Physics1-2.Number and Magnitude1-3.Directed Numbers1-4.The Inner Product1-5.The Outer Product1-6.Synthesis and Simplification1-7.Axioms for Geometric AlgebraChapter 2: Developments in Geometric Algebra2-1.Basic Identities and Definitions2-2.The Algebra of a Euclidean Plane2-3.The Algebra of Euclidean 3-Space2-4.Directions, Projections and Angles2-5.The Exponential Function2-6.Analytic Geometry2-7.Functions of a Scalar Variable2-8.Directional Derivatives and Line IntegralsChapter 3: Mechanics of a Single Particle3-1.Newton's Program3-2.Constant Force3-3.Constant Force with Linear Drag3-4.Constant Force with Quadratic Drag3-5.Fluid Resistance3-6.Constant Magnetic Field3-7.Uniform Electric and Magnetic Fields3-8.Linear Binding Force3-9.Forced Oscillations3-10.Conservative Forces and ConstraintsChapter 4: Central Forces and Two-Particle Systems4-1.Angular Momentum4-2.Dynamics from Kinematics4-3.The Kepler Problem4-4.The Orbit in Time4-5.Conservative Central Forces4-6.Two-particle Systems4-7.Elastic Collisions4-8.Scattering Cross SectionsChapter 5: Operators and Transformations5-1.Linear Operators and Matrices5-2.Symmetric and Skewsymmetric Operators5-3.The Arithmetic of Reflections and Rotations5-4.Transformation Groups5-5.Rigid Motions and Frames of Reference5-6.Motion in Rotating SystemsChapter 6: Many-Particle Systems6-1.General Properties of Many-Particle Systems6-2.The Method of Lagrange6-3.Coupled Oscillations and Waves6-4.Theory of Small Oscillations6-5.The Newtonian Many Body ProblemChapter 7: Rigid Body Mechanics7-1.Rigid Body Modeling7-2.Rigid Body Structure7-3.The Symmetrical Top7-4.Integrable Cases of Rotational Motion7-5.Rolling Motion7-6.Impulsive MotionChapter 8: Celestial Mechanics8-1.Gravitational Forces, Fields and Torques8-2.Perturbations of Kepler Motion8-3.Perturbations in the Solar System8-4.Spinor Mechanics and Perturbation TheoryChapter 9: Relativistic Mechanics9-1.Spacetime and Its Representations9-2.Spacetime Maps and Measurements9-3.Relativistic Particle Dynamics9-4.Energy-Momentum Conservation9-5.Relativistic Rigid Body MechanicsAppendixA Spherical TrigonometryB Elliptic FunctionsC Units, Constants and DataHints and Solutions for Selected ExercisesReferencesIndex
· · · · · · (收起)