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The Geometry of Ordinary Variational Equations

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...

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Bibliographic Details
Main Author: Krupkova, Olga
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1997, 1997
Edition:1st ed. 1997
Series:Lecture Notes in Mathematics
Subjects:
Mechanics, Applied
Geometry, Differential
Mathematical Analysis
Engineering Mechanics
Analysis
Manifolds (mathematics)
Differential Geometry
Global Analysis (mathematics)
Global Analysis And Analysis On Manifolds
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a The Geometry of Ordinary Variational Equations  |h Elektronische Ressource  |c by Olga Krupkova 
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505 0 |a 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. 
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653 |a Engineering Mechanics 
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653 |a Differential Geometry 
653 |a Global analysis (Mathematics) 
653 |a Global Analysis and Analysis on Manifolds 
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490 0 |a Lecture Notes in Mathematics 
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082 0 |a 515 
520 |a 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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