Introduction to Mechanics and Symmetry
A Basic Exposition of Classical Mechanical Systems
Sofort lieferbar | Lieferzeit: Sofort lieferbar I
ISBN-13:
9780387986432
Veröffentl:
1999
Erscheinungsdatum:
01.01.1999
Seiten:
586
Autor:
Jerrold E. Marsden
Gewicht:
1055 g
Format:
241x162x40 mm
Serie:
17, Texts in Applied Mathematics
Sprache:
Deutsch
Beschreibung:
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.
Symmetry's role in mechanics has always been important. In recent times, this aspect 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. The new edition of this book, which lays the basic foundations for these topics, including reduction theory along with specific applications, has been extensively updated and includes new illustrations and exercises.
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.
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