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.
General
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