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AuthorMarsden, Jerrold E. author
TitleIntroduction to Mechanics and Symmetry [electronic resource] : A Basic Exposition of Classical Mechanical Systems / by Jerrold E. Marsden, Tudor S. Ratiu
ImprintNew York, NY : Springer New York : Imprint: Springer, 1999
Edition Second Edition
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Descript XVIII, 586 p. online resource


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 specific 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 makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text 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 on-line


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 Lieโ{128}{148}Poisson and Eulerโ{128}{148}Poincarรฉ Reduction -- 14 Coadjoint Orbits -- 15 The Free Rigid Body -- References

Physics Topological groups Lie groups Manifolds (Mathematics) Complex manifolds Physics Theoretical Mathematical and Computational Physics Topological Groups Lie Groups Manifolds and Cell Complexes (incl. Diff.Topology)


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