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 HamiltonJacobi equation, and the Liouville Theorem on solutions of the HamiltonJacobi 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.

Presents a precise definition and examples of the symmetries of a Hamiltonian, including transformations that depend explicitly on the time Contains the definition and examples of R-separable solutions of the Hamilton-Jacobi equation Illustrates a complete and simplified proof for the Liouville Theorem and examples of its application Includes a complete list of detailed solutions for self-study students

Autorentext

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.

Inhalt
Preface.- The Lagrangian Formalism.- Some Applications of the Lagrangian Formalism.- Rigid Bodies.- The Hamiltonian Formalism.- Canonical Transformations.- The HamiltonJacobi Formalism.- Solutions.- References.- Index.