Reduced dynamics and Lagrangian submanifolds of symplectic manifolds

Abstract

In this paper, we will see that the symplectic creed by Weinstein "everything is a Lagrangian submanifold" also holds for Hamilton-Poincaré and Lagrange-Poincaré reduction. In fact, we show that solutions of the Hamilton-Poincaré equations and of the Lagrange-Poincaré equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction.

26 pages

References in corpus (1)

• Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations

Cited by in corpus (6)

• Large values of cusp forms on GL(n)
• On the Geometry of the Hamilton-Jacobi Equation and Generating Functions
• Regularity properties of fiber derivatives associated with higher-order mechanical systems
• Reduction of pre-Hamiltonian actions
• Contact Dynamics versus Legendrian and Lagrangian Submanifolds
• Hamilton-Dirac systems for charged particles in gauge fields