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Table of Contents
Acknowledgements; Contents; Symbols; 1 Introduction; 2 Lagrangian Mechanics; 2.1 Lagrangian Mechanical Systems and their Equations of Motion; 2.2 Integrals of Motion; 2.3 Motion in a Radial Potential; 2.3.1 Motion in Newton's Gravitational Potential; 3 Hamiltonian Mechanics; 3.1 Symplectic Geometry and Hamiltonian Systems; 3.2 Relation between Lagrangian and Hamiltonian Systems; 3.2.1 Hamiltonian Formulation for the Lagrangian Systems of Example 2.32.3; 3.2.2 The Legendre Transform; 3.3 Linearization and Stability; 4 Hamilton
Jacobi Theory; 5 Classical Field Theory
5.1 The Lagrangian, the Action and the Euler
Lagrange Equations5.2 Automorphisms and Conservation Laws; 5.3 Why are Conservation Laws called Conservation Laws?; 5.4 Examples of Field Theories; 5.4.1 Sigma Models; 5.4.2 Pure Yang
Mills Theory; 5.4.3 The Einstein
Hilbert Lagrangian; 5.5 The Energy-Momentum Tensor; Appendix A Exercises; A.1 Exercises for Chap.2; A.2 Exercises for Chap.3; A.3 Exercises for Chap.4; A.4 Exercises for Chap.5; Appendix References; ; Index
Jacobi Theory; 5 Classical Field Theory
5.1 The Lagrangian, the Action and the Euler
Lagrange Equations5.2 Automorphisms and Conservation Laws; 5.3 Why are Conservation Laws called Conservation Laws?; 5.4 Examples of Field Theories; 5.4.1 Sigma Models; 5.4.2 Pure Yang
Mills Theory; 5.4.3 The Einstein
Hilbert Lagrangian; 5.5 The Energy-Momentum Tensor; Appendix A Exercises; A.1 Exercises for Chap.2; A.2 Exercises for Chap.3; A.3 Exercises for Chap.4; A.4 Exercises for Chap.5; Appendix References; ; Index