Introduction to Mechanics and Symmetry

A Basic Exposition of Classical Mechanical Systems

Jerrold E. Marsden, Tudor S. Ratiu (Autoren)

Buch | Hardcover

586 Seiten

1999 | 2nd ed. 1999
Springer-Verlag New York Inc.
978-0-387-98643-2 (ISBN)

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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 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 Lie—Poisson and Euler—Poincaré Reduction.- 14 Coadjoint Orbits.- 15 The Free Rigid Body.- References.

Reihe/Serie	Texts in Applied Mathematics ; 17
Zusatzinfo	XVIII, 586 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
ISBN-10	0-387-98643-X / 038798643X
ISBN-13	978-0-387-98643-2 / 9780387986432
Zustand	Neuware