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Symplectic Geometry and Analytical Mechanics - Charles-Michel Marle
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Charles-Michel Marle:

Symplectic Geometry and Analytical Mechanics - gebonden uitgave, pocketboek

1987, ISBN: 9027724385

[EAN: 9789027724380], Neubuch, [SC: 0.0], [PU: Springer Netherlands], GEOMETRIE; RAUMLEHRE; HOST; LEMMA; VECTORFIELD; BOUNDARYELEMENTMETHOD; CALCULUS; CLASS; CONSTANT; ELECTRICALENGINEERI… Meer...

NEW BOOK. Verzendingskosten:Versandkostenfrei. (EUR 0.00) AHA-BUCH GmbH, Einbeck, Germany [51283250] [Rating: 5 (von 5)]
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Symplectic Geometry and Analytical Mechanics P. Libermann Author
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Symplectic Geometry and Analytical Mechanics P. Libermann Author - nieuw boek

ISBN: 9789027724380

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find… Meer...

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Symplectic Geometry and Analytical Mechanics P. Libermann Author
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Symplectic Geometry and Analytical Mechanics P. Libermann Author - nieuw boek

ISBN: 9789027724380

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find… Meer...

new in stock. Verzendingskosten:zzgl. Versandkosten., exclusief verzendingskosten
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Symplectic Geometry and Analytical Mechanics - Marle, Charles-Michel;Libermann, P.
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Marle, Charles-Michel;Libermann, P.:
Symplectic Geometry and Analytical Mechanics - nieuw boek

ISBN: 9789027724380

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find… Meer...

Nr. 21615873. Verzendingskosten:Does not ship to your country., exclusief verzendingskosten
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Symplectic Geometry and Analytical Mechanics
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Symplectic Geometry and Analytical Mechanics - nieuw boek

ISBN: 9789027724380

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find… Meer...

Nr. 978-90-277-2438-0. Verzendingskosten:Worldwide free shipping, , DE. (EUR 0.00)

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Symplectic Geometry and Analytical Mechanics P. Libermann Author

.. although orginally written in French, the translation by B.E. Schwartzbach is very good and the exposition thorough and careful. This book is a welcome addition to the literature. It will surely prove useful as a reference...' Bulletin of the American Mathematical Society, Vol.20 No. 1, Jan.1989

Gedetalleerde informatie over het boek. - Symplectic Geometry and Analytical Mechanics P. Libermann Author


EAN (ISBN-13): 9789027724380
ISBN (ISBN-10): 9027724385
Gebonden uitgave
Verschijningsjaar: 2007
Uitgever: Springer Netherlands Core >2 >T
542 Bladzijden
Gewicht: 0,976 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2007-05-29T10:17:19+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2024-02-06T19:54:12+01:00 (Amsterdam)
ISBN/EAN: 9789027724380

ISBN - alternatieve schrijfwijzen:
90-277-2438-5, 978-90-277-2438-0
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: annemies tamboer, marle, paulette libermann, liberman, paul michel, michel charles, van gulik
Titel van het boek: symplectic geometry and analytical mechanics


Gegevens van de uitgever

Auteur: P. Libermann; Charles-Michel Marle
Titel: Mathematics and Its Applications; Symplectic Geometry and Analytical Mechanics
Uitgeverij: Springer; Springer Netherland
526 Bladzijden
Verschijningsjaar: 1987-03-31
Dordrecht; NL
Taal: Engels
192,59 € (DE)
197,99 € (AT)
212,50 CHF (CH)
Available
XVI, 526 p.

BB; Hardcover, Softcover / Mathematik/Geometrie; Geometrie; Verstehen; Host; Lemma; Vector field; boundary element method; calculus; class; constant; electrical engineering; equation; foliation; graphs; integral; lie group; measure; programming; Geometry; BC; EA

I. Symplectic vector spaces and symplectic vector bundles.- 1: Symplectic vector spaces.- 1. Properties of exterior forms of arbitrary degree.- 2. Properties of exterior 2-forms.- 3. Symplectic forms and their automorphism groups.- 4. The contravariant approach.- 5. Orthogonality in a symplectic vector space.- 6. Forms induced on a vector subspace of a symplectic vector space.- 7. Additional properties of Lagrangian subspaces.- 8. Reduction of a symplectic vector space. Generalizations.- 9. Decomposition of a symplectic form.- 10. Complex structures adapted to a symplectic structure.- 11. Additional properties of the symplectic group.- 2: Symplectic vector bundles.- 12. Properties of symplectic vector bundles.- 13. Orthogonality and the reduction of a symplectic vector bundle.- 14. Complex structures on symplectic vector bundles.- 3: Remarks concerning the operator ? and Lepage’s decomposition theorem.- 15. The decomposition theorem in a symplectic vector space.- 16. Decomposition theorem for exterior differential forms.- 17. A first approach to Darboux’s theorem.- II. Semi-basic and vertical differential forms in mechanics.- 1. Definitions and notations.- 2. Vector bundles associated with a surjective submersion.- 3. Semi-basic and vertical differential forms.- 4. The Liouville form on the cotangent bundle.- 5. Symplectic structure on the cotangent bundle.- 6. Semi-basic differential forms of arbitrary degree.- 7. Vector fields and second-order differential equations.- 8. The Legendre transformation on a vector bundle.- 9. The Legendre transformation on the tangent and cotangent bundles.- 10. Applications to mechanics: Lagrange and Hamilton equations.- 11. Lagrange equations and the calculus of variations.- 12. The Poincaré-Cartan integral invariant.- 13.Mechanical systems with time dependent Hamiltonian or Lagrangian functions.- III. Symplectic manifolds and Poisson manifolds.- 1. Symplectic manifolds; definition and examples.- 2. Special submanifolds of a symplectic manifold.- 3. Symplectomorphisms.- 4. Hamiltonian vector fields.- 5. The Poisson bracket.- 6. Hamiltonian systems.- 7. Presymplectic manifolds.- 8. Poisson manifolds.- 9. Poisson morphisms.- 10. Infinitesimal automorphisms of a Poisson structure.- 11. The local structure of Poisson manifolds.- 12. The symplectic foliation of a Poisson manifold.- 13. The local structure of symplectic manifolds.- 14. Reduction of a symplectic manifold.- 15. The Darboux-Weinstein theorems.- 16. Completely integrable Hamiltonian systems.- 17. Exercises.- IV. Action of a Lie group on a symplectic manifold.- 1. Symplectic and Hamiltonian actions.- 2. Elementary properties of the momentum map.- 3. The equivariance of the momentum map.- 4. Actions of a Lie group on its cotangent bundle.- 5. Momentum maps and Poisson morphisms.- 6. Reduction of a symplectic manifold by the action of a Lie group.- 7. Mutually orthogonal actions and reduction.- 8. Stationary motions of a Hamiltonian system.- 9. The motion of a rigid body about a fixed point.- 10. Euler’s equations.- 11. Special formulae for the group SO(3).- 12. The Euler-Poinsot problem.- 13. The Euler-Lagrange and Kowalevska problems.- 14. Additional remarks and comments.- 15. Exercises.- V. Contact manifolds.- 1. Background and notations.- 2. Pfaffian equations.- 3. Principal bundles and projective bundles.- 4. The class of Pfaffian equations and forms.- 5. Darboux’s theorem for Pfaffian forms and equations.- 6. Strictly contact structures and Pfaffian structures.- 7. Protectable Pfaffian equations.- 8. Homogeneous Pfaffianequations.- 9. Liouville structures.- 10. Fibered Liouville structures.- 11. The automorphisms of Liouville structures.- 12. The infinitesimal automorphisms of Liouville structures.- 13. The automorphisms of strictly contact structures.- 14. Some contact geometry formulae in local coordinates.- 15. Homogeneous Hamiltonian systems.- 16. Time-dependent Hamiltonian systems.- 17. The Legendre involution in contact geometry.- 18. The contravariant point of view.- Appendix 1. Basic notions of differential geometry.- 1. Differentiable maps, immersions, submersions.- 2. The flow of a vector field.- 3. Lie derivatives.- 4. Infinitesimal automorphisms and conformai infinitesimal transformations.- 5. Time-dependent vector fields and forms.- 6. Tubular neighborhoods.- 7. Generalizations of Poincaré’s lemma.- Appendix 2. Infinitesimal jets.- 1. Generalities..- 2. Velocity spaces.- 3. Second-order differential equations.- 4. Sprays and the exponential mapping.- 5. Covelocity spaces.- 6. Liouville forms on jet spaces.- Appendix 3. Distributions, Pfaffian systems and foliations.- 1. Distributions and Pfaffian systems.- 2. Completely integrable distributions.- 3. Generalized foliations defined by families of vector fields.- 4. Differentiable distributions of constant rank.- Appendix 4. Integral invariants.- 1. Integral invariants of a vector field.- 2. Integral invariants of a foliation.- 3. The characteristic distribution of a differential form.- Appendix 5. Lie groups and Lie algebras.- 1. Lie groups and Lie algebras; generalities.- 2. The exponential map.- 3. Action of a Lie group on a manifold.- 4. The adjoint and coadjoint representations.- 5. Semi-direct products.- 6. Notions regarding the cohomology of Lie groups and Lie algebras.- 7. Affine actions of Lie groups and Liealgebras.- Appendix 6. The Lagrange-Grassmann manifold.- 1. The structure of the Lagrange-Grassmann manifold.- 2. The signature of a Lagrangian triplet.- 3. The fundamental groups of the symplectic group and of the Lagrange-Grassmann manifold.- Appendix 7. Morse families and Lagrangian submanifolds.- 1. Lagrangian submanifolds of a cotangent bundle.- 2. Hamiltonian systems and first-order partial differential equations.- 3. Contact manifolds and first-order partial differential equations.- 4. Jacobi’s theorem.- 5. The Hamilton-Jacobi equation for autonomous systems.- 6. The Hamilton-Jacobi equation for non autonomous systems.

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