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Lagrangian and Hamiltonian Dynamics

Peter Mann

June 2018

ISBN: 9780198822387

560 pages
Paperback
246x189mm

In Stock

Price: £29.99

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.

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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.

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