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2013, ISBN: 9789027724397
Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 1987, 548 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: NUSTBK20171230-C0103163,… Meer...
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1987, ISBN: 9027724393
[EAN: 9789027724397], Neubuch, [SC: 0.0], [PU: Springer Netherlands], PROGRAMMING; HOST; LEMMA; VECTORFIELD; BOUNDARYELEMENTMETHOD; CALCULUS; CLASS; CONSTANT; ELECTRICALENGINEERING; EQUAT… Meer...
Libermann, P.; Marle, Charles-Michel:
Symplectic Geometry and Analytical Mechanics (Mathematics and Its Applications, 35) - pocketboek1987, ISBN: 9027724393
[EAN: 9789027724397], Gebraucht, guter Zustand, [PU: Springer], A+ Customer service! Satisfaction Guaranteed! Book is in Used-Good condition. Pages and cover are clean and intact. Used it… Meer...
Symplectic Geometry and Analytical Mechanics (Mathematics and Its Applications, 35, Band 35) - pocketboek
2013
ISBN: 9789027724397
Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 1987, 548 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: NUSTBK20171230-C0103163,… Meer...
2013, ISBN: 9027724393
[EAN: 9789027724397], Neubuch, [PU: Springer 2013-10-04], Books
ISBN: 9789027724397
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Gedetalleerde informatie over het boek. - Symplectic Geometry and Analytical Mechanics (Mathematics and Its Applications, 35, Band 35)
EAN (ISBN-13): 9789027724397
ISBN (ISBN-10): 9027724393
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pocket book
Verschijningsjaar: 2013
Uitgever: Springer
Boek bevindt zich in het datenbestand sinds 2007-06-12T21:47:55+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2023-12-15T20:41:40+01:00 (Amsterdam)
ISBN/EAN: 9789027724397
ISBN - alternatieve schrijfwijzen:
90-277-2439-3, 978-90-277-2439-7
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: schwarzbach, paulette libermann, liberman, marle, michel charles, van gulik
Titel van het boek: symplectic geometry and analytical mechanics, mathematics 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.
BC; 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; BB
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.Andere boeken die eventueel grote overeenkomsten met dit boek kunnen hebben:
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