V.I. Arnold's Mathematical Methods of Classical Mechanics is entirely based on the ideas and methods of symplectic geometry, such as the Birkhoff normal form, the Kolmogorov- Arnold-Moser theorem on the persistence of invariant tori, and the intersection theory of Lagrangian submanifolds.

Arnold Weinstein points out that the first symplectic submanifold was already introduced "avant la lettre" by Lagrange in 1808. Weinstein goes on to state what he calls the symplectic creed that Everything is a Lagrangian submanifold --- how that underlies classical mechanics is discussed in this MO question.

V.I. Arnold's Mathematical Methods of Classical Mechanics is entirely based on the ideas and methods of symplectic geometry, such as the Birkhoff normal form, the Kolmogorov- Arnold-Moser theorem on the persistence of invariant tori, and the intersection theory of Lagrangian submanifolds.

Alan Weinstein points out that the first symplectic submanifold was already introduced "avant la lettre" by Lagrange in 1808. Weinstein goes on to state what he calls the symplectic creed that Everything is a Lagrangian submanifold --- how that underlies classical mechanics is discussed in this MO question.

V.I. Arnold's Mathematical Methods of Classical Mechanics is entirely based on the ideas and methods of symplectic geometry, such as the Birkhoff normal form, the Kolmogorov- Arnold-Moser theorem on the persistence of invariant tori, and the intersection theory of Lagrangian submanifolds.

Arnold Weinstein points out that the first symplectic submanifold was already introduced "avant la lettre" by Lagrange in 1808.

V.I. Arnold's Mathematical Methods of Classical Mechanics is entirely based on the ideas and methods of symplectic geometry, such as the Birkhoff normal form, the Kolmogorov- Arnold-Moser theorem on the persistence of invariant tori, and the intersection theory of Lagrangian submanifolds.

Arnold Weinstein points out that the first symplectic submanifold was already introduced "avant la lettre" by Lagrange in 1808. Weinstein goes on to state what he calls the symplectic creed that Everything is a Lagrangian submanifold --- how that underlies classical mechanics is discussed in this MO question.