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.

This book is a collection of survey articles in a broad field of the geometrical theory of the calculus of variations and its applications in analysis, geometry and physics. It is a commemorative volume to celebrate the sixty-fifth birthday of Professor Krupa, one of the founders of modern geometric variational theory, and a major contributor to this topic and its applications over the past thirty-five years. All the authors invited to contribute to this volume have established high reputations in their field. The book will exclusively provide a variety of important results, techniques and applications that are usually available only by consulting original papers in many different journals. It will be of interest to researchers in variational calculus, mathematical physics and the other related areas of differential equations, natural operators and geometric structures. Also, it will become an important source of current research for doctoral students and postdoctorals in these fields.