Symplectic integrators do not, in general, reproduce all the features of the dynamics of the Hamiltonian systems which they approximate. For example, energy conservation is lost, and global features such as separatrices can be destroyed. We study these effects for a Hamiltonian system with a single degree of freedom and the simplest possible symplectic integrator. We look at a sequence of Hamil...

Bifurcation of limit cycles in a cubic Hamiltonian system with quintic perturbed terms is investigated using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the perturbed cubic Hamiltonian system. The study reveals firstly that there are at most 15 limit cycles in the cubic Hamiltonian system with pertur...

In this paper, we study the interconnection of two robots, which are modeled as port-controlled Hamiltonian systems through a transmission line with time delay. There will be no analysis of the time delay, but its presence justifies the use of scattering variables to preserve passivity. The contributions of the paper are twofold: first, a geometrical, multidimensional, power-consistent expositi...

The problem of moment matching with preservation of port Hamiltonian and gradient structure is studied. Based on the time-domain approach to linear moment matching, we characterize the (subset of) port Hamiltonian/gradient models from the set of parameterized models that match the moments of a given port Hamiltonian/gradient system, at a set of finite points.

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence r...

Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving interconnection of Dirac structures is again a Dirac structure. In this paper we study interconnection prop...

In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters ma...

First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to KirchhoWs laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using ...

We present a method of generating Magri-Morosi-Gel'fand-Dorfman's (MMGD) bi-Hamiltonian structure leading to complete integrability of the associated Hamilto-nian system and discuss its applicability to study finite-dimensional Hamiltonian systems from the bi-Hamiltonian point of view. The approach is applied to the finite-dimensional, non-periodic Toda lattice.

This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns perturbations of the uncoupled system consisting of the simple pendulum and the harmonic oscillator. We show that small coupling perturbations with, possibly, the addition of positive and negative dampin...