Modeling of Systems With Position-Dependent Mass Revisited: A Port-Hamiltonian Approach
Authors
Dimitri Jeltsema, Arnau Dòria-Cerezo
Abstract
It is known that straightforward application of the classical Lagrangian and Hamiltonian formalism to systems with mass varying explicitly with position may lead to discrepancies in the formulation of the equations of motion. Systems with mass varying explicitly with position often arise from situations where the partitioning of a closed system of constant mass leads to open subsystems that exchange mass among themselves. One possible solution is to introduce additional nonconservative generalized forces that account for these effects. However, it remains unclear how to systematically interconnect the Lagrangian or Hamiltonian subsystems. In this note, systems with mass varying explicitly with position and their properties are studied in the port-Hamiltonian modeling framework. The port-Hamiltonian formalism combines the classical Lagrangian and Hamiltonian approach with network modeling and is applicable to various engineering domains. One of the strong aspects of the port-Hamiltonian formalism is that power-preserving interconnections between port-Hamiltonian subsystems results in another port-Hamiltonian system with composite energy and interconnection structure. The motion of a heavy cable being deployed from a reel by the action of gravity is used as an example.
Citation
- Journal: Journal of Applied Mechanics
- Year: 2011
- Volume: 78
- Issue: 6
- Pages:
- Publisher: ASME International
- DOI: 10.1115/1.4003910
BibTeX
@article{Jeltsema_2011,
title={{Modeling of Systems With Position-Dependent Mass Revisited: A Port-Hamiltonian Approach}},
volume={78},
ISSN={1528-9036},
DOI={10.1115/1.4003910},
number={6},
journal={Journal of Applied Mechanics},
publisher={ASME International},
author={Jeltsema, Dimitri and Dòria-Cerezo, Arnau},
year={2011}
}
References
- Cveticanin, L. Dynamics of Machines with Variable Mass. (2022) doi:10.1201/9780203759066 – 10.1201/9780203759066
- Crellin, E. B., Janssens, F., Poelaert, D., Steiner, W. & Troger, H. On Balance and Variational Formulations of the Equation of Motion of a Body Deploying Along a Cable. Journal of Applied Mechanics vol. 64 369–374 (1997) – 10.1115/1.2787316
- Pesce, C. P., Tannuri, E. A. & Casetta, L. The Lagrange equations for systems with mass varying explicitly with position: some applications to offshore engineering. Journal of the Brazilian Society of Mechanical Sciences and Engineering vol. 28 496–504 (2006) – 10.1590/s1678-58782006000400015
- Pesce, C. P. The Application of Lagrange Equations to Mechanical Systems With Mass Explicitly Dependent on Position. Journal of Applied Mechanics vol. 70 751–756 (2003) – 10.1115/1.1601249
- van der Schaft. L2-Gain and Passivity Techniques in Nonlinear Control
- Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
- Abraham. Foundations of Mechanics
- Ray, J. R. Lagrangians and systems they describe—how not to treat dissipation in quantum mechanics. American Journal of Physics vol. 47 626–629 (1979) – 10.1119/1.11767