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Classical mechanics. Field theory --- Differential geometry. Global analysis --- Algebres convexes --- Convex domains --- Convexe algebra's --- Hamiltonian systems --- Hamiltonsystemen --- Systèmes hamiltoniens --- Algèbres convexes --- Algèbres convexes --- Systèmes hamiltoniens

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Algebraic geometry --- Abelian varieties --- Abelse varieteiten --- Hamiltonian systems --- Hamiltonsystemen --- Systèmes hamiltoniens --- Varieties Abelian --- Variétés abéliennes --- Abelian varieties. --- Hamiltonian systems. --- Differentiable dynamical systems --- Dynamique différentiable --- Differentiable dynamical systems. --- Dynamique différentiable --- Systèmes hamiltoniens --- Equations differentielles sur une variete --- Geometrie algebrique --- Varietes abeliennes

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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.

Differential equations --- Differential equations. --- Calculus of variations. --- Hamiltonian systems. --- Calculus of variations --- Hamiltonian systems --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Calcul des variations --- Differentiaalvergelijkingen --- Equations différentielles --- Hamiltonsystemen --- Systèmes hamiltoniens --- Variatieberekening --- Mathematical analysis. --- Analysis (Mathematics). --- Differential geometry. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mechanics. --- Mechanics, Applied. --- Analysis. --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Theoretical and Applied Mechanics. --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential geometry --- 517.1 Mathematical analysis --- Mathematical analysis --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory