Introduction to Mechanics and Symmetry
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Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability, and bifurcation, and the study of specific rigid, fluid, plasma, and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which make it accessible to a wide variety of readers, especially senior undergraduate and graduate students in mathematics, physics, and engineering.
PrefaceAbout the Authors1Introduction and Overview12Hamiltonian Systems on Linear Symplectic Spaces613An Introduction to Infinite-Dimensional Systems1054Manifolds, Vector Fields, and Differential Forms1215Hamiltonian Systems on Symplectic Manifolds1476Cotangent Bundles1657Lagrangian Mechanics1818Variational Principles, Constraints, & Rotating Systems2199An Introduction to Lie Groups26510Poisson Manifolds32711Momentum Maps36512Computation and Properties of Momentum Maps38313Lie - Poisson and Euler - Poincare Reduction41514Coadjoint Orbits44315The Free Rigid Body481References519Index553
