Introduction to Mechanics and Symmetry

• 1 Introduction and Overview.- 2 Hamiltonian Systems on Linear Symplectic Spaces.- 3 An Introduction to Infinite-Dimensional Systems.- 4 Manifolds, Vector Fields, and Differential Forms.- 5 Hamiltonian Systems on Symplectic Manifolds.- 6 Cotangent Bundles.- 7 Lagrangian Mechanics.- 8 Variational Principles, Constraints, & Rotating Systems.- 9 An Introduction to Lie Groups.- 10 Poisson Manifolds.- 11 Momentum Maps.- 12 Computation and Properties of Momentum Maps.- 13 Lie—Poisson and Euler—Poincaré Reduction.- 14 Coadjoint Orbits.- 15 The Free Rigid Body.- References.

"The book is self-contained.It remains a good and solid introduction to this subject." Nieuw Archief voor Wiskunde, March 2001 "... This book takes the reader on one of the greatest journeys in modern mathematics that has as its roots a subject that is more than 300 years old. Armed with this knowledge a reader is ready to pursue numerous topics of active mathematical research, from the more pure domains of symplectic geometry and topology to the geometric analysis of the limitless supply of examples from mechanics." Newsletter of the Newzealand Mathematical Society, No. 81, April 2001 Second Edition J.E. Marsden and T.S. Ratiu Introduction to Mechanics and Symmetry A Basic Exposition of Classical Mechanical Systems "As the name of the book implies, a consistent theme running through the book is that of symmetry. Indeed the latter half of the book focuses on Poisson manifolds, momentum maps, Lie-Poisson reduction, co-adjoint orbits and the integrability of the rigid body. The discussion of reduction must be the most comprehensive yet given. A pleasant feature of the book is that most of the theory that relates to finite-dimensional mechanical systems is illustrated concretely in terms of local coordinates, thereby making the book accessible even to beginners in the field."-MATHEMATICAL REVIEWS