The Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupková.
Material type: TextSeries: Lecture Notes in Mathematics ; 1678Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1997Description: CCLXIV, 254 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540696575Subject(s): Mathematics | Global analysis | Global differential geometry | Mechanics, applied | Mathematics | Differential Geometry | Global Analysis and Analysis on Manifolds | Theoretical and Applied MechanicsAdditional physical formats: Printed edition:: No titleDDC classification: 516.36 LOC classification: QA641-670Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1820 |
Basic geometric tools -- Lagrangean dynamics on fibered manifolds -- Variational Equations -- Hamiltonian systems -- Regular Lagrangean systems -- Singular Lagrangean systems -- Symmetries of Lagrangean systems -- Geometric intergration 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.
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