03402nam 22007695 450 991014629600332120260128234053.03-540-69657-110.1007/BFb0093438(CKB)1000000000437335(SSID)ssj0000323521(PQKBManifestationID)12072464(PQKBTitleCode)TC0000323521(PQKBWorkID)10300016(PQKB)10118355(DE-He213)978-3-540-69657-5(MiAaPQ)EBC5595560(MiAaPQ)EBC6700624(Au-PeEL)EBL5595560(OCoLC)1076236160(Au-PeEL)EBL6700624(PPN)155175130(EXLCZ)99100000000043733520121227d1997 u| 0engurnn#008mamaatxtccrThe Geometry of Ordinary Variational Equations /by Olga Krupkova1st ed. 1997.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1997.1 online resource (CCLXIV, 254 p.)Lecture Notes in Mathematics,1617-9692 ;1678Bibliographic Level Mode of Issuance: Monograph3-540-63832-6 Includes bibliographical references and index.Basic geometric tools -- Lagrangean dynamics on fibered manifolds -- Variational Equations -- Hamiltonian systems -- Regular Lagrangean systems -- Singular Lagrangean systems -- Symmetries of Lagrangean systems -- Geometric integration methods -- Lagrangean systems on ?: R×M»R.The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.Lecture Notes in Mathematics,1617-9692 ;1678Mathematical analysisGeometry, DifferentialGlobal analysis (Mathematics)Manifolds (Mathematics)Mechanics, AppliedAnalysisDifferential GeometryGlobal Analysis and Analysis on ManifoldsEngineering MechanicsMathematical analysis.Geometry, Differential.Global analysis (Mathematics)Manifolds (Mathematics)Mechanics, Applied.Analysis.Differential Geometry.Global Analysis and Analysis on Manifolds.Engineering Mechanics.515Krupková Olga1960-61656MiAaPQMiAaPQMiAaPQBOOK9910146296003321Geometry of ordinary variational equations78087UNINA