Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

Abstract

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.

33 pages

References in corpus (3)

• Non-holonomic constrained systems as implicit differential equations
• Discrete dynamics in implicit form
• Symplectic integrators in sub-Riemannian geometry: the Martinet case

Cited by in corpus (6)

• Retraction maps: a seed of geometric integrators
• Geometric Constrained Variational Calculus. I. - Piecewise smooth extremals
• Dirac Structures in Vakonomic Mechanics
• Regularity properties of fiber derivatives associated with higher-order mechanical systems
• Morse families in optimal control problems
• Hamilton-Dirac systems for charged particles in gauge fields