The Geometry of Ordinary Variational Equations
Krupková, Olga.
The Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupková. - CCLXIV, 254 p. online resource. - Lecture Notes in Mathematics, 1678 0075-8434 ; . - Lecture Notes in Mathematics, 1678 .
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.
9783540696575
10.1007/BFb0093438 doi
Global analysis (Mathematics).
Global differential geometry.
Global analysis.
Mechanics, applied.
Analysis.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Theoretical and Applied Mechanics.
QA299.6-433
515
The Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupková. - CCLXIV, 254 p. online resource. - Lecture Notes in Mathematics, 1678 0075-8434 ; . - Lecture Notes in Mathematics, 1678 .
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.
9783540696575
10.1007/BFb0093438 doi
Global analysis (Mathematics).
Global differential geometry.
Global analysis.
Mechanics, applied.
Analysis.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Theoretical and Applied Mechanics.
QA299.6-433
515