Title: The geometry of ordinary variational equations
First published: 1997
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.
Subjects: Differential equations, Calculus of variations, Hamiltonian systems, Mathematics, Global analysis (Mathematics), Global differential geometry, Mechanics, applied
LC classification: QA3 .L28 no. 1678, QA372 .L28 no. 1678