Lagrangian and Hamiltonian Dynamics

Description

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.

• Informal style with numerous fresh, modern and inter-disciplinary applications (including medicine, biology, chemistry)
• Fully worked problems and mathematical backgrounds
• Thoughtful illustrations and highlighted equations

About the Author(s)

Peter Mann, St Andrews University, UK

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.

Table of Contents

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

Additional Resources

A solutions manual is available for this title. Please click here to order your copy.