Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Exergetic Port-Hamiltonian Systems for Multibody Dynamics

Markus Lohmayer, Giuseppe Capobianco, Sigrid Leyendecker

TL;DR

The paper presents Exergetic Port-Hamiltonian Systems (EPHS) as a compositional framework for multiphysics multibody dynamics, enabling modular construction of large assemblies via energy-domain interconnections. It develops a geometric foundation based on Lie groups and left-trivialized velocities, and builds primitive subsystems for energy storage and exchange that enforce thermodynamic consistency through Dirac and Onsager structures. The authors formulate explicit EPHS models for rigid bodies and joints, including kinetic/potential energy storage, gyroscopic effects, holonomic constraints, friction, and environmental interactions, and derive the dynamics via a variational Lagrange-d'Alembert-Pontryagin approach that matches classical principle results. This approach supports reusable, hierarchical model components and thermodynamically sound interconnections, offering a scalable, safe path to large-scale multiphysics simulations with potential discretization and extension to flexible bodies.

Abstract

Multibody dynamics simulation plays an important role in various fields, including mechanical engineering, robotics, and biomechanics. Setting up computational models however becomes increasingly challenging as systems grow in size and complexity. Especially the consistent combination of models across different physical domains usually demands a lot of attention. This motivates us to study formal languages for compositional modeling of multiphysical systems. This article shows how multibody systems, or more precisely assemblies of rigid bodies connected by lower kinematic pairs, fit into the framework of Exergetic Port-Hamiltonian Systems (EPHS). This approach is based on the hierarchical decomposition of systems into their ultimately primitive components, using a simple graphical syntax. Thereby, cognitive load can be reduced and communication is facilitated, even with non-experts. Moreover, the encapsulation and reuse of subsystems promotes efficient model development and management. In contrast to established modeling languages such as Modelica, the primitive components of EPHS are not defined by arbitrary equations. Instead, there are four kinds of components, each defined by a particular geometric structure with a clear physical interpretation. This higher-level approach could make the process of building and maintaining large-scale models simpler and also safer.

Exergetic Port-Hamiltonian Systems for Multibody Dynamics

TL;DR

The paper presents Exergetic Port-Hamiltonian Systems (EPHS) as a compositional framework for multiphysics multibody dynamics, enabling modular construction of large assemblies via energy-domain interconnections. It develops a geometric foundation based on Lie groups and left-trivialized velocities, and builds primitive subsystems for energy storage and exchange that enforce thermodynamic consistency through Dirac and Onsager structures. The authors formulate explicit EPHS models for rigid bodies and joints, including kinetic/potential energy storage, gyroscopic effects, holonomic constraints, friction, and environmental interactions, and derive the dynamics via a variational Lagrange-d'Alembert-Pontryagin approach that matches classical principle results. This approach supports reusable, hierarchical model components and thermodynamically sound interconnections, offering a scalable, safe path to large-scale multiphysics simulations with potential discretization and extension to flexible bodies.

Abstract

Multibody dynamics simulation plays an important role in various fields, including mechanical engineering, robotics, and biomechanics. Setting up computational models however becomes increasingly challenging as systems grow in size and complexity. Especially the consistent combination of models across different physical domains usually demands a lot of attention. This motivates us to study formal languages for compositional modeling of multiphysical systems. This article shows how multibody systems, or more precisely assemblies of rigid bodies connected by lower kinematic pairs, fit into the framework of Exergetic Port-Hamiltonian Systems (EPHS). This approach is based on the hierarchical decomposition of systems into their ultimately primitive components, using a simple graphical syntax. Thereby, cognitive load can be reduced and communication is facilitated, even with non-experts. Moreover, the encapsulation and reuse of subsystems promotes efficient model development and management. In contrast to established modeling languages such as Modelica, the primitive components of EPHS are not defined by arbitrary equations. Instead, there are four kinds of components, each defined by a particular geometric structure with a clear physical interpretation. This higher-level approach could make the process of building and maintaining large-scale models simpler and also safer.
Paper Structure (38 sections, 76 equations, 7 figures)

This paper contains 38 sections, 76 equations, 7 figures.

Table of Contents

  1. Introduction
  2. EPHS modeling language
  3. Related work
  4. Outline
  5. EPHS modeling language by example
  6. Geometric foundation
  7. Physical space and coordinate frames
  8. Configuration of a rigid body
  9. Lie group structure of the configuration space
  10. Geometric interpretation of composition
  11. Material velocity
  12. The derivative (interlude)
  13. Dual spaces and dual maps (another interlude)
  14. Trivialized velocity variables
  15. Adjoint actions
  16. ...and 23 more sections

Figures (7)

  • Figure 1: Interconnection pattern for a basic multibody system consisting of two bodies $\mathtt{b_1}$ and $\mathtt{b_2}$ connected by a joint $\mathtt{j}$.
  • Figure 2: Interconnection pattern for the rigid body model. Box $\mathtt{pe}$ represents storage of potential energy, while box $\mathtt{ke}$ represents storage of kinetic energy. Box $\mathtt{pkc}$ represents the reversible coupling of the potential and kinetic energy domains. Box $\mathtt{lp}$ represents the gyroscopic effects (Lie-Poisson structure).
  • Figure 3: Interconnection pattern for the joint model. Box $\mathtt{hc}$ represents the holonomic constraint describing the joint kinematics. Boxes $\mathtt{o_1}$ and $\mathtt{o_2}$ take into account the offset between the reference frame of one of the connected bodies and the reference frame defining the respective joint force application point. Box $\mathtt{pe}$ represents a possible storage of potential energy, depending on the relative pose of the two connected bodies. Box $\mathtt{pkc}$ represents the coupling between the potential and kinetic energy domains of the joint. Box $\mathtt{mf}$ represents the irreversible process of mechanical friction and box $\mathtt{env}$ represents the environment which directly absorbs the generated heat.
  • Figure 4: Flattened interconnection pattern for the basic multibody system. The pattern is obtained by substituting the pattern in \ref{['fig:body']} into the inner boxes $\mathtt{b_1}$ and $\mathtt{b_2}$ of the pattern in \ref{['fig:mbs']} and further by substituting the pattern in \ref{['fig:joint']} into the inner box $\mathtt{j}$.
  • Figure 5: Interconnection pattern for a mechanical oscillator model. Box $\mathtt{pe}$ represents storage of potential energy. Box $\mathtt{ke}$ represents storage of kinetic energy. Box $\mathtt{pkc}$ represents the reversible coupling between the potential energy domain, represented by the junction on its left, and the kinetic energy domain represented by the junction on its right. The outer port $\mathtt{p}$ exposes the kinetic energy domain.
  • ...and 2 more figures