Lagrangian & Hamiltonian Dynamics /
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| Format: | eBook |
| Language: | English |
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Oxford, United Kingdom :
Oxford University Press,
2018.
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| Edition: | First edition. |
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Lagrangian & Hamiltonian Dynamics; Copyright; Dedication; Contents; Preface; Part I: Newtonian Mechanics; 1: Newton's Three Laws; 1.1 Phase Space; 1.2 Systems of Particles; 1.3 The N-body Problem; Chapter summary; 2: Energy and Work; Chapter summary; 3: Introductory Rotational Dynamics; Chapter summary; 4: The Harmonic Oscillator; Chapter summary; 5: Wave Mechanics & Elements ofMathematical Physics; Part II: Lagrangian Mechanics; 6: Coordinates & Constraints; Chapter summary; 7: The Stationary Action Principle; 7.1 The Inverse Problem
- 7.2 Higher-Order Theories & the Ostrogradsky Equation7.3 The Second Variation; 7.4 Functions & Functionals; 7.5 Boundary Conditions; 7.6 Variations; 7.7 Weierstrass-Erdmann Conditions for Broken Extremals; 7.8 Hamilton-Suslov Principle; Chapter summary; 8: Constrained Lagrangian Mechanics; 8.1 Holonomic Constraints; 8.2 Non-Holonomic Constraints; Chapter summary; 9: Point Transformations in Lagrangian Mechanics; Chapter summary; 10: The Jacobi Energy Function; Chapter summary; 11: Symmetries & Lagrangian-Hamilton-Jacobi Theory; 11.1 Noether's Theorem; 11.2 Gauge Theory
- 11.3 Isotropic Symmetries11.4 Caratheodory-Hamilton-Jacobi theory; Chapter summary; 12: Near-Equilibrium Oscillations; 12.1 Normal Modes; Chapter summary; 13: Virtual Work & d'Alembert's Principle; 13.1 Gauss's Least Constraint & Jourdain's Principle; 13.2 The Gibbs-Appell Equations; Chapter summary; Part III: Canonical Mechanics; 14: The Hamiltonian & Phase Space; Chapter summary; 15: Hamilton's Principle in Phase Space; Chapter summary; 16: Hamilton's Equations & RouthianReduction; 16.1 Phase Space Conservation Laws; 16.2 Routhian Mechanics; 17: Poisson Brackets & AngularMomentum
- 17.1 Poisson Brackets & Angular Momenta17.2 Poisson Brackets & Symmetries; Chapter summary; 18: Canonical & Gauge Transformations; 18.1 Canonical Transformations I; 18.2 Canonical Transformations II; 18.3 In nitesimal Canonical Transformations; Chapter summary; 19: Hamilton-Jacobi Theory; 19.1 Hamilton-Jacobi Theory I; 19.2 Hamilton-Jacobi Theory II; Chapter summary; 20: Liouville's Theorem & ClassicalStatistical Mechanics; 20.1 Liouville's Theorem & the Classical Propagator; 20.2 Koopman-von Neumann Theory; 20.3 Classical Statistical Mechanics; 20.4 Symplectic Integrators; Chapter summary
- 21: Constrained Hamiltonian DynamicsChapter summary; 22: Autonomous Geometrical Mechanics; 22.1 A Coordinate-Free Picture; 22.2 Poisson Manifolds & Symplectic Reduction; 22.3 Geometrical Lagrangian Mechanics; 22.4 Elements of Constrained Geometry; Chapter summary; 23: The Structure of Phase Space; 23.1 Time-Dependent Geometrical Mechanics; 23.2 Picturing Phase Space; Chapter summary; 24: Near-Integrable Systems; 24.1 Canonical Perturbation Theory; 24.2 KAM Theory & Elements of Chaos; Part IV: Classical Field Theory; 25: Lagrangian Field Theory; Chapter summary; 26: Hamiltonian Field Theory