Discrete variational Hamiltonian mechanics

S. Lall and M. West

Journal of Physics A: Mathematical and General 39(19), 5509-5519, 2006.

The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms.

DOI: 10.1088/0305-4470/39/19/S11

Full text: LaWe2006.pdf