The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me­ chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Manifolds, tensor analysis, and applications (Global analysis, pure and applied)

Science & Math

MARSDEN, Jerrold E.

Abraham, Ralph

Ratiu, Tudor S.

Mathematics

Longman Higher Education

Introduction to mechanics and symmetry: A basic exposition of classical mechanical systems (Texts in applied mathematics)

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 emphasize the role of symmetry in various aspects of mechanics. In recent times, this feature has accelerated because of new applications of symmetry techniques for studying integrable and chaotic systems, stability and bifurcation, as well as for obtaining new insight into specific rigid, fluid, plasma and elastic systems. Mechanics and Symmetry lays the basic foundation for these topics. It also covers reduction theory and includes numerous specific applications, making it beneficial to physicists and engineers. Unlike the competition, this text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, especially senior undergraduate and graduate students in mathematics, physics and engineering.

Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Texts in Applied Mathematics)

Computers & Technology

Programming

Springer, Verlag

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.

Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Texts in Applied Mathematics, 17)

Springer

This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial differential equations. The papers collected in this volume reflect these fruitful ties as well as some others, strengthened over the last two decades, with areas of applied science including control theory.

Mechanics Day Proceedings

Krishna, Perinkulam Sambamurthy

Shadwick, W.F.

Amer Mathematical Society

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.

Marsden, Jerrold E. E.

* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds.* Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

Momentum Maps and Hamiltonian Reduction (Progress in Mathematics)

Ortega, Juan-Pablo

Birkhauser

This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.

Hamiltonian Reduction by Stages (Lecture Notes in Mathematics, Vol. 1913) (Lecture Notes in Mathematics, 1913)

Misiolek, Gerard

Perlmutter, Matthew

Reference

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