| Description |
1 online resource (xvi, 515 pages) : illustrations (some color) |
| Series |
Oxford texts in applied and engineering mathematics ; 12 |
|
Oxford texts in applied and engineering mathematics ; 12.
|
| Contents |
Lagrangian and Hamiltonian mechanics -- Manifolds -- Geometry on manifolds -- Mechanics on manifolds -- Lie groups and Lie algebras -- Group actions, symmetries, and reduction -- Euler-Poincaré 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-Poincaré image matching -- Continuum equations with advection -- Euler-Poincaré 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 |
| Bibliography |
Includes bibliographical references (pages 504-508) and index |
| Notes |
Print version record |
| Subject |
Mechanics.
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Geometry.
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Symmetry (Mathematics)
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mechanics (physics)
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geometry.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Mechanics -- Solids.
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Geometry
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Mechanics
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Symmetry (Mathematics)
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| Form |
Electronic book
|
| Author |
Schmah, Tanya.
|
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Stoica, Cristina, 1967-
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| ISBN |
9780191549861 |
|
019154986X |
|
0199212902 |
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9780199212903 |
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0199212910 |
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9780199212910 |
|
