Introduction to Mechanics and Symmetry: An Initial Exploration of Classical Mechanical Systems

Author: (USA) Marsden, (USA) Ratiu, translated by Wang Lijin et al.
Publisher:
Publish Date: 2006-08-01
Features: This book elaborates on the theory and progress of mechanics and symmetry, combining the geometric perspective of mechanics with solid analysis. It conducts an in-depth study of fundamental issues in mechanics, such as variational principles and Hamiltonian structures in continuum mechanics, fluid dynamics, plasma physics, etc. It provides useful tools for specific models, such as new stability and bifurcation criteria based on energy-Casimir and energy-momentum methods, new numerical codes based on update procedures with geometric precision and variational integrators, as well as new retargeting techniques in control theory and robotics. The book introduces the widespread application of symmetry in mechanics, including its use in reduction, stability, bifurcation, the destruction of symmetry of solutions with respect to the symmetry group of a given system, finding explicit solutions for integrable systems, and gaining an in-depth understanding of special systems (e.g., the Kowalewski top). This English edition of the book is accompanied by a solutions guide and online supplements, providing readers with important related knowledge. Both authors, Professor Marsden from the California Institute of Technology (USA) and Professor Ratiu from the University of California, Santa Cruz, and the Swiss Federal Institute of Technology (Switzerland), are internationally renowned experts in their respective fields. They present the fundamental theories of mechanics and symmetry from a rich perspective, offering readers comprehensive and detailed theoretical and applied analyses.