| Description |
1 online resource |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Preface; Table of Contents; Figures; Biographical details; I: Galilean relativity and Newtonian physics; 1: Introduction; 1.1 Fundamental particles and interactions; 1.2 Electrodynamics; 1.3 Weak-nuclear interaction; 1.4 Strong-nuclear interaction; 1.5 Gravity; 1.6 Unifying principles; 2: Space and time; 2.1 Space; 2.2 Time; 2.3 Spacetime coordinates; 2.4 Homogeneity, isotropy and curvature; 2.5 Orient ability of time and space; 3: Euclidean geometry; 3.1 Euclidean line elements; 3.2 Indexed notation and matrix multiplication |
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3.3 Parity3.4 Charge conjugation; 3.5 Time reversal; 3.6 Rotations; 3.7 Groups; 4: Tensor fields in Euclidean spacetime; 4.1 Euclidean scalars and scalar fields; 4.2 Euclidean vectors and vector fields; 4.3 Euclidean tensors and tensor fields; 4.4 Symmetric and antisymmetric tensors; 4.5 Proper and improper tensors; 4.6 Permutation pseudotensor; 4.7 Three-dimensional tensor duality; 4.8 Manifest Euclidean covariance; 5: Spacetime kinematics and Galilean relativity; 5.1 Introduction; 5.2 Measurement and simultaneity; 5.3 Spacetime reference frame; 5.4 Principle of relativity |
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5.5 Galilean and Lorentz transformations5.6 Galilean relativity; 5.7 Aristotelean and Galilean gravity; 5.8 Fibre bundle structure of Galilean spacetime; 6: Newtonian mechanics; 6.1 Newtonian dynamics and conservation; 6.2 Additivity of conserved quantities; 6.3 Interaction in Newtonian physics; 6.4 Potential energy of conservative systems; 6.5 External interaction; 6.6 Galilean covariance and conservation; 6.7 Natural equations; 7: Newtonian gravity; 7.1 Introduction; 7.2 Gravity; 7.3 Newtonâ#x80;#x99;s gravity theory; 7.4 Newtonâ#x80;#x99;s gravitation constant; 7.5 Field equations of Newtonian gravity |
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7.6 First-order Newtonian gravity field equations7.7 Second-order Newtonian gravity field equations; 7.8 Equations of motion in a gravitational field; 7.9 Cosmological constant; 7.10 Gauge freedom of Newtonian gravity; 7.11 Weak equivalence principle; 7.12 Michell and Laplace black holes; 7.13 Soldnerâ#x80;#x99;s gravitational deflection of light; 7.14 Deviations from Newtonian gravity; 7.15 Newton-Cartan spacetime; II: Lagrangian interaction and symmetry; 8: Euler-Lagrange equations of motion; 8.1 Introduction; 8.2 Lagrangian of a system of Newtonian particles |
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8.3 Momenta and configuration space Hamiltonian8.4 Generalized coordinates in mechanics; 8.5 Stationary action; 8.6 Hamiltonâ#x80;#x99;s principle of stationary action; 8.7 Functional differentiation; 8.8 Lagrangian interaction; 8.9 Newtonian gravitational Lagrangian interaction; 8.10 Constraints; 9: Symmetries and Noetherâ#x80;#x99;s theorem; 9.1 Introduction; 9.2 Point transformations of configuration space; 9.3 Invariant and covariant Lagrangians; 9.4 Hamiltonâ#x80;#x99;s modified principle of varied action; 9.5 Symmetries of Lagrangian systems; 9.6 Noether charges for mechanical systems |
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9.7 Noetherâ#x80;#x99;s theorem for mechanical systems |
| Summary |
This book is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed March 15, 2018) |
| Subject |
Electrodynamics.
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Gravitation.
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Relativity (Physics)
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Symmetry (Physics)
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SCIENCE -- Physics -- Electricity.
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SCIENCE -- Physics -- Electromagnetism.
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Electrodynamics
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Gravitation
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Relativity (Physics)
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Symmetry (Physics)
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| Form |
Electronic book
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| ISBN |
9780429493539 |
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0429493533 |
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9780429973161 |
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0429973160 |
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