An Introduction to Hamiltonian Mechanics. 1st ed. 2018

種類:

電子ブック

責任表示:

by Gerardo F. Torres del Castillo

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• Torres del Castillo, Gerardo F.
• SpringerLink (Online service)

シリーズ名:

Birkhäuser Advanced Texts Basler Lehrbücher ;

ISBN:

9783319952253 [3319952250]    

注記:

Preface -- The Lagrangian Formalism -- Some Applications of the Lagrangian Formalism -- Rigid Bodies -- The Hamiltonian Formalism -- Canonical Transformations -- The Hamilton–Jacobi Formalism -- Solutions -- References -- Index.
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 c

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