Lagrangian and Hamiltonian Dynamics

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Lagrangian and Hamiltonian Dynamics

Mann, Peter

ウェブストア価格 ¥21,584（本体¥19,622）
Oxford University Press（2018/06発売）
外貨定価 US$ 105.00
ポイント 196pt

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製本 Hardcover:ハードカバー版／ページ数 560 p.
言語 ENG
商品コード 9780198822370
DDC分類 515.39

Full Description

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.

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 & Elements of Mathematical Physics
Part II: Langrangian Mechanics
7: Introduction
8: Coordinates & Constraints
9: The Stationary Action Principle
10: Constrained Langrangian Mechanics
11: Point Transformations in Langrangian Mechanics
12: The Jacobi Energy Function
13: Symmetries & Langrangian-Hamiltonian-Jacobi Theory
14: Near-Equilibrium Oscillations
15: Virtual Work & d'Alembert's Principle
Part III: Canonical Mechanics
16: Introduction
17: The Hamiltonian & Phase Space
18: Hamiltonian's equations & Routhian Reduction
19: Poisson Brackets & Angular momentum
20: Canonical & Gauge Transformations
21: Hamilton-Jacobi Theory
22: Liouville's Theorem & 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 & Nambu Brackets Explored
Appendix: Canonical Transformations Explored
Appendix F: Action-Angle Variables Explored
Appendix G: Statistical Mechanics Explored
Appendix H: Biographies