En savoir plus
The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
Table des matières
- Part I: Newtonian Mechanics
- 1: Introduction
- 2: Newton's Three Laws
- 3: Energy and Work
- 4: Introductory Rotational Dynamics
- 5: The Harmonic Oscillator
- 6: Wave Mechanics and Elements of Mathematical Physics
- Part II: Langrangian Mechanics
- 7: Introduction
- 8: Coordinates and Constraints
- 9: The Stationary Action Principle
- 10: Constrained Langrangian Mechanics
- 11: Point Transformations in Langrangian Mechanics
- 12: The Jacobi Energy Function
- 13: Symmetries and Langrangian-Hamiltonian-Jacobi Theory
- 14: Near-Equilibrium Oscillations
- 15: Virtual Work and d'Alembert's Principle
- Part III: Canonical Mechanics
- 16: Introduction
- 17: The Hamiltonian and Phase Space
- 18: Hamiltonian's equations and Routhian Reduction
- 19: Poisson Brackets and Angular momentum
- 20: Canonical and Gauge Transformations
- 21: Hamilton-Jacobi Theory
- 22: Liouville's Theorem and Classical Statistical Mechanics
- 23: Constrained Hamiltonian Dynamics
- 24: Autonomous Geometrical Mehcanics
- 25: The Structure of Phase Space
- 26: Near-Integrable Systems
- Part IV: Classical Field Theory
- 27: Introduction
- 28: Langrangian Field Theory
- 29: Hamiltonian Field Theory
- 30: Clssical Electromagnetism
- 31: Neother's Theorem for Fields
- 32: Classical Path-Integrals
- Part V: Preliminary Mathematics
- 33: The (Not so?) Basics
- 34: Matrices
- 35: Partial Differentiation
- 36: Legendre Transformations
- 37: Vector Calculus
- 38: Differential equations
- 39: Calculus of Variations
- Part VI: Advanced Mathematics
- 40: Linear Algebra
- 41: Differential Geometry
- Part VII: Exam Style Questions
- Appendix A: Noether's Theorem Explored
- Appendix B: The Action Principle Explored
- Appendix C: Useful Relations
- Appendxi D: Poisson and Nambu Brackets Explored
- Appendix: Canonical Transformations Explored
- Appendix F: Action-Angle Variables Explored
- Appendix G: Statistical Mechanics Explored
- Appendix H: Biographies
A propos de l'auteur
Peter Mann completed his undergraduate degree in Chemistry at the University of St Andrews. He is now a PhD student at the University of St Andrews investigating spreading phenomena on complex networks and how antibiotic resistance proliferates on different network topologies.
Résumé
The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
