Lagrangian and Hamiltonian Dynamics

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Beschreibung

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers.

Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications.

The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

Über den Autor

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.

Inhaltsverzeichnis

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

Details

Erscheinungsjahr:	2018
Fachbereich:	Astronomie
Genre:	Importe , Physik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780198822387
ISBN-10:	0198822383
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Mann, Peter
Hersteller:	Oxford University Press
Verantwortliche Person für die EU:	Deutsche Bibelgesellschaft, Postfach:81 03 40, D-70567 Stuttgart, vertrieb@dbg.de
Maße:	247 x 189 x 32 mm
Von/Mit:	Peter Mann
Erscheinungsdatum:	05.06.2018
Gewicht:	1,154 kg