Peter Mann

Lagrangian and Hamiltonian Dynamics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 544
• Erscheinungstermin: 10. Mai 2018
• Englisch
• ISBN-13: 9780192555410
• Artikelnr.: 54582795

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