The geometry of ordinary variational equations
By: Olga Krupková.
Series: Lecture notes in mathematics ;; 1678; Lecture notes in mathematics (Springer-Verlag) ;; 1678.
Publisher: Springer-Verlag
Published: 1997
Place of publication: Berlin; New York
Language: eng
Number of pages: 251
Subjects: Differential equations; Calculus of variations; Hamiltonian systems
Description: 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.
Notes: Includes bibliographical references (p. [229]-245) and index.