New Foundations for Classical Mechanics
This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1986, 1986
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| Edition: | 1st ed. 1986 |
| Series: | Fundamental Theories of Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 3–10. Conservative Forces and Constraints
- 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
- 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
- 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 BodyProblem
- 7: Rigid Body Mechanics
- 7–1. Rigid Body Modeling
- 7–2. Rigid Body Structure
- 7–3. The Symmetrical Top
- 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
- 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
- 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
- 7–4. Integrable Cases of Rotational Motion
- 7–5. Rolling Motion
- 7–6. Impulsive Motion
- 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
- 9: Foundations of Mechanics
- 9–1. Models and Theories
- 9–2. The Zeroth Law of Physics
- 9–3. Generic Laws and Principles of Particle Mechanics
- 9–4. Modeling Processes
- Appendixes
- A Spherical Trigonometry
- B Elliptic Functions
- C Units, Constants and Data
- Hints and Solutions for Selected Exercises
- References