Author | Krupkovรก, Olga. author |
---|---|

Title | The Geometry of Ordinary Variational Equations [electronic resource] / by Olga Krupkovรก |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1997 |

Connect to | http://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