An Introduction to Hamiltonian Mechanics

Gerardo F. Torres del Castillo

ISBN 10: 3319952242 / ISBN 13: 9783319952246

Editore: Springer International Publishing, Springer International Publishing, 2018

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Druck auf Anfrage Neuware - Printed after ordering - This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises.For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton-Jacobi equation, and the Liouville Theorem on solutions of the Hamilton-Jacobi equation.Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The textassumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.

Codice articolo 9783319952246

Dati bibliografici

• Titolo: An Introduction to Hamiltonian Mechanics
• Editore: Springer International Publishing, Springer International Publishing
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 3319952242
• ISBN 13: 9783319952246
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 25 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 25 millimetri di profondità
• Peso: 797 grammi

Descrizione articolo

Riassunto

This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises.

For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton–Jacobi equation, and the Liouville Theorem on solutions of the Hamilton–Jacobi equation. 

Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.

Informazioni sull?autore

Gerardo F. Torres del Castillo is a professor of physics and mathematics at the Universidad Autónoma de Puebla, where he has taught since 1979. He is the author or coauthor of more than 30 papers on classical mechanics. His other published books are Differentiable Manifolds; 3-D Spinors, Spin-Weighted Functions and their Applications; and Spinors in Four-Dimensional Spaces.