Lagrangian and Hamiltonian Dynamics

ISBN : 9780198822370

Peter Mann
560 ページ
189 x 246 mm

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics with a relaxed and self-contained setting for those unacquainted with mathematics or university level physics. 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.


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


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.