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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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The geometry of ordinary variational equations, Olga Krupková
- Sprache
- Erscheinungsdatum
- 1997
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- Titel
- The geometry of ordinary variational equations
- Sprache
- Englisch
- Autor*innen
- Olga Krupková
- Verlag
- Springer
- Verlag
- 1997
- ISBN10
- 3540638326
- ISBN13
- 9783540638322
- Kategorie
- Mathematik
- Beschreibung
- 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.