Peter Mann

Lagrangian and Hamiltonian Dynamics

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 560
• Erscheinungstermin: 5. Juni 2018
• Englisch
• Abmessung: 247mm x 189mm x 32mm
• Gewicht: 1154g
• ISBN-13: 9780198822387
• ISBN-10: 0198822383
• Artikelnr.: 50847003

Autorenporträt

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.

Inhaltsangabe

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