Olga Krupkova 
Geometry of Ordinary Variational Equations [PDF ebook] 

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.