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Geometric mechanics and symmetry [electronic resource] / Darryl D. Holm, Tanya Schmah, Cristina Stoica ; with solutions to selected exercises by David C.P. Ellis.

By: Holm, Darryl D.
Contributor(s): Schmah, Tanya | Stoica, Cristina, 1967-.
Material type: TextTextSeries: Oxford texts in applied and engineering mathematics: 12.Publisher: New York : Oxford University Press, 2009Description: 1 online resource (xvi, 515 p.) : ill. (some col.).ISBN: 9780191549861 (electronic bk.); 019154986X (electronic bk.).Subject(s): Mechanics | Geometry | Symmetry (Mathematics) | SCIENCE -- Mechanics -- General | SCIENCE -- Mechanics -- SolidsGenre/Form: Electronic books. | Electronic books.Additional physical formats: Print version:: Geometric mechanics and symmetry.DDC classification: 531.01/516 Online resources: EBSCOhost
Contents:
Lagrangian and Hamiltonian mechanics -- Manifolds -- Geometry on manifolds -- Mechanics on manifolds -- Lie groups and Lie algebras -- Group actions, symmetries, and reduction -- Euler-Poincar�e reduction : rigid body and heavy top -- Momentum maps -- Lie-Poisson reduction -- Pseudo-rigid bodies -- EPDiff -- EPDiff solution behavior -- Integrability of EPDiff in 1D -- EPDiff in n dimensions -- Computational anatomy : contour matching using EPDiff -- Computational anatomy : Euler-Poincar�e image matching -- Continuum equations with advection -- Euler-Poincar�e theorem for geophysical fluid dynamics.
Summary: Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such asn-particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and S.
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Includes bibliographical references (p. 504-508) and index.

Lagrangian and Hamiltonian mechanics -- Manifolds -- Geometry on manifolds -- Mechanics on manifolds -- Lie groups and Lie algebras -- Group actions, symmetries, and reduction -- Euler-Poincar�e reduction : rigid body and heavy top -- Momentum maps -- Lie-Poisson reduction -- Pseudo-rigid bodies -- EPDiff -- EPDiff solution behavior -- Integrability of EPDiff in 1D -- EPDiff in n dimensions -- Computational anatomy : contour matching using EPDiff -- Computational anatomy : Euler-Poincar�e image matching -- Continuum equations with advection -- Euler-Poincar�e theorem for geophysical fluid dynamics.

Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such asn-particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and S.

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