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OverviewAn 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. Full Product DetailsAuthor: Peter Mann (St Andrews University, UK)Publisher: Oxford University Press Imprint: Oxford University Press Dimensions: Width: 18.90cm , Height: 2.60cm , Length: 24.60cm Weight: 1.166kg ISBN: 9780198822387ISBN 10: 0198822383 Pages: 560 Publication Date: 05 June 2018 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsPart 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: BiographiesReviewsAuthor InformationPeter 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. Tab Content 6Author Website:Countries AvailableAll regions |
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