Linear Hamiltonian behaviors and bilinear differential forms

We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study systems described by higher-order differential equations, thus dispensing with the usual point of view in classical mechanics of considering first- and second-order differential equations only

Hamiltonian and Variational Linear Distributed Systems

We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary linear constant-coefficient differential equations is Hamiltonian if and only if it is variational. In this paper we extend this result to systems described by linear, constant-coefficient partial differential equations. It is shown that any variational system is Hamiltonian, and that any scalar Hamiltonian system is contained (in general, properly) in a particular variational system

Interpolation with bilinear differential forms

We present a recursive algorithm for modeling with bilinear differential forms. We discuss applications of this algorithm for interpolation with symmetric bivariate polynomials, and for computing storage functions for autonomous systems

Quantum and Classical Aspects of Deformed c=1c=1 Strings.

The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in $c<1$ strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique, and leads to several different perturbative interpretations of this model as a string theory. Two such possible interpretations are examined. In both cases, the classical limit of the string equations, which turns out to give a formal solution of Polchinski's scattering equations, shows that the classical scattering amplitudes of massless tachyons are insensitive to deformations of the parameters in the matrix model.Comment: 52 pages, Latex

Port-Hamiltonian systems: an introductory survey

The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models

Conserved- and zero-mean quadratic quantities in oscillatory systems

We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems

Model Reduction for Controllable Systems

In the papers [1], [7] a new scheme for passivity-preserving model reduction has been proposed. We have shown in [2] that the approach can also be interpreted from a dissipativity theory point of view, and we put forward two procedures in order to compute a driving variable or output nulling representation of a reduced order model for a given behavior. In this paper we illustrate improved versions of both algorithms, which produce a controllable reduced-order model. The new algorithms are based on several original results of independent interest