Time-discretization of Hamiltonian dynamical systems
Difference equations for Hamiltonian systems are derived from a discrete variational principle (DTH -- discrete time Hamiltonian). This article is focused on the basic ideas of DTH dynamics for the case of autonomous systems with one degree of freedom. Variational principles of mechanical systems are recalled in section 2. Section 3 introduces notation for describing piecewise-linear, continuous functions. In the next section the DTH principle of stationary action is discussed and applied to DTH dynamics. Simulation results for two Newtonian potential systems are presented in section 6, and section 7 presents, without proofs, some extensions to nonautonomous systems with \(n\)-degrees of freedom.
scientific article; zbMATH DE number 699056