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Related papers: Port-Hamiltonian systems on discrete manifolds

200 papers

The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (pHs), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac…

Analysis of PDEs · Mathematics 2020-10-07 Andrea Brugnoli , Daniel Alazard , Valérie Pommier-Budinger , Denis Matignon

We study the geometric structure of port-Hamiltonian systems. Starting with the intuitive understanding that port-Hamiltonian systems are "in between" certain closed Hamiltonian systems, the geometric structure of port-Hamiltonian systems…

Mathematical Physics · Physics 2024-06-04 Jonas Kirchhoff , Bernhard Maschke

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.

Numerical Analysis · Mathematics 2023-03-15 Alexandre Anahory Simoes , David Martín de Diego , Bernhard Maschke

We analyze infinite-dimensional Hamiltonian systems corresponding to partial differential equations on one-dimensional spatial domains formulated with formally skew-adjoint Hamiltonian operators and nonlinear Hamiltonian density. In various…

Analysis of PDEs · Mathematics 2024-01-30 Till Preuster , Manuel Schaller , Bernhard Maschke

The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…

Dynamical Systems · Mathematics 2022-01-19 Volker Mehrmann , Benjamin Unger

We give insight in the structure of port-Hamiltonian systems as control systems in between two closed Hamiltonian systems. Using the language of category theory, we identify systems with their behavioural representation and view a…

Dynamical Systems · Mathematics 2024-06-04 Jonas Kirchhoff

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known…

Optimization and Control · Mathematics 2021-07-29 Markus Schöberl , Andreas Siuka

The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…

Mathematical Physics · Physics 2025-05-01 Katarzyna Grabowska , Michalina Borczyńska , Joanna Majsak , Tomasz Sobczak

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

Symplectic Geometry · Mathematics 2019-04-03 A. Lesfari

In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly…

Probability · Mathematics 2022-05-12 Francesco Cordoni , Luca Di Persio , Riccardo Muradore

We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.

Analysis of PDEs · Mathematics 2022-03-14 Federico Califano , Ramy Rashad , Frederic P. Schuller , Stefano Stramigioli

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution…

Mathematical Physics · Physics 2018-02-14 François Gay-Balmaz , Hiroaki Yoshimura

A new formulation for the modular construction of flexible multibody systems is presented. By rearranging the equations for a flexible floating body and introducing the appropriate canonical momenta, the model is recast into a coupled…

Classical Physics · Physics 2020-10-07 Andrea Brugnoli , Daniel Alazar , Valérie Pommier-Budinger , Denis Matignon

We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a…

Numerical Analysis · Mathematics 2026-04-14 Antoine Bendimerad-Hohl , Ghislain Haine , Laurent Lefèvre , Denis Matignon

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…

Symplectic Geometry · Mathematics 2007-05-23 Yarema A. Prykarpatsky , Anatoliy M. Samoilenko

This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…

Numerical Analysis · Mathematics 2025-12-09 Ignacio Diaz Alastuey , Yann Le Gorrec , Yongxin Wu

This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and, then, we extend it to the nonlinear setting…

Mathematical Physics · Physics 2023-03-10 Álvaro Rodríguez Abella , Melvin Leok

Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…

Numerical Analysis · Mathematics 2020-06-09 Andrea Brugnoli , Daniel Alazard , Valérie Pommier-Budinger , Denis Matignon

Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. This manuscript presents a discrete-time pH descriptor formulation for linear, completely causal, scattering passive dynamical systems…

Optimization and Control · Mathematics 2023-10-18 Karim Cherifi , Hannes Gernandt , Dorothea Hinsen , Volker Mehrmann

We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical…

High Energy Physics - Theory · Physics 2024-06-04 Ignacio S. Gomez , Vipul Kumar Pandey , Ronaldo Thibes