The Geometry of Ordinary Variational Equations: 1678 (Lecture Notes in Mathematics, 1678) - Softcover

Krupkova, Olga

 
9783540638322: The Geometry of Ordinary Variational Equations: 1678 (Lecture Notes in Mathematics, 1678)

Synopsis

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.

"synopsis" may belong to another edition of this title.

Synopsis

This study of the geometry of ordinary variational equations examines: basic geometric tools; Langrangian dynamics on fibered manifolds; regular Langrangian systems; geometric integration methods; and more.

"About this title" may belong to another edition of this title.