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AuthorKrupkovรก, Olga. author
TitleThe Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupkovรก
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1997
Connect tohttp://dx.doi.org/10.1007/BFb0093438
Descript CCLXIV, 254 p. online resource

SUMMARY

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


CONTENT

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 ?: Rร{151}MยปR


Mathematics Mathematical analysis Analysis (Mathematics) Global analysis (Mathematics) Manifolds (Mathematics) Differential geometry Mechanics Mechanics Applied Mathematics Analysis Differential Geometry Global Analysis and Analysis on Manifolds Theoretical and Applied Mechanics



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