Port-Hamiltonian modeling of rigid multibody systems

Authors

Thomas Berger, René Hochdahl, Timo Reis, Robert Seifried

Abstract

We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as well as gyroscopic effects. The resulting equations take the form of nonlinear differential-algebraic equations that inherently preserve an energy balance. We show that the proposed class is closed under interconnection, and we provide several examples to illustrate the theory.

Keywords

Port-Hamiltonian systems; Multibody systems; Position and velocity constraints; Dirac structures; Lagrangian submanifolds; Resistive relations; Differential-algebraic equations; 34A09; 37J39; 53D12; 70E55; 93C10

Citation

• Journal: Nonlinear Dynamics
• Year: 2025
• Volume: 113
• Issue: 23
• Pages: 32037–32058
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s11071-025-11776-y

BibTeX

@article{Berger_2025,
  title={{Port-Hamiltonian modeling of rigid multibody systems}},
  volume={113},
  ISSN={1573-269X},
  DOI={10.1007/s11071-025-11776-y},
  number={23},
  journal={Nonlinear Dynamics},
  publisher={Springer Science and Business Media LLC},
  author={Berger, Thomas and Hochdahl, René and Reis, Timo and Seifried, Robert},
  year={2025},
  pages={32037--32058}
}

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References

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