Global Aspects of Classical Integrable Systems

Book Details

• Author: Cushman, Richard H.

• Brand: Birkhäuser

• Edition: 2nd

• Binding: Hardcover

• Number of Pages: 477

• Release Date: 11-06-2015

• ISBN: 9783034809177

• Package Dimensions: 9.1 x 6.2 x 1.3 inches

• Languages: English

About the Book

"Energy-Momentum Mapping and Symmetry Reduction" by Richard H. Cushman offers a comprehensive exploration of the geometry behind the energy-momentum mapping of five classical integrable systems. These systems are integral to the study of advanced classical mechanics and global analysis, specifically for graduate students and professional mathematicians.

The book provides a complete description of the geometry for systems such as:

• The 2-dimensional harmonic oscillator

• The geodesic flow on the 3-sphere

• The Euler top

• The spherical pendulum

• The Lagrange top

This work is remarkable for its presentation of symmetry reduction theory, a topic rarely tackled in such detail. Cushman introduces a general theory of symmetry reduction that helps reduce symmetries in systems like the spherical pendulum and Lagrange top, enhancing the understanding of their behavior. The book also calculates the monodromy obstruction to the existence of global action-angle coordinates for these systems, which is an advanced topic in mathematical physics.

While the book focuses on mathematical rigor, its clear explanations make it suitable as a textbook for those interested in classical mechanics, dynamical systems, and global analysis.

Key Features:

• In-depth Analysis: Describes the energy-momentum mapping for five classical systems in detail.

• Symmetry Reduction: Introduces a general theory of symmetry reduction, with applications to the spherical pendulum and Lagrange top.

• Monodromy Obstruction: Explores monodromy obstruction and global action-angle coordinates for certain mechanical systems.

• Target Audience: Professional mathematicians and graduate students in classical mechanics or global analysis.

Review

This second edition of Cushman’s work is highly regarded for its mathematical depth and clarity in tackling complex topics within classical mechanics. The inclusion of symmetry reduction and monodromy obstruction adds unique insights that make it an essential reference for anyone looking to deepen their understanding of advanced classical dynamics and integrable systems.