Mechanical memory elements: Modeling of systems with position-dependent mass revisited
Authors
Dimitri Jeltsema, Arnau Doria-Cerezo
Abstract
The purpose of this paper is two-fold. First, it is shown that systems in which mass is changing with position belong to the family of memory elements. Memory elements have originally been introduced in the electrical domain to provide a logical extension of the resistor, inductor, and capacitor. Secondly, it is shown that straightforward application of the classical Lagrangian and Hamiltonian frameworks to describe these type of elements generally leads to erroneous results. To overcome these problems, a port-Hamiltonian formulation is proposed. The developments are illustrated and motivated using the elementary cable-reel system.
Citation
- Journal: 49th IEEE Conference on Decision and Control (CDC)
- Year: 2010
- Volume:
- Issue:
- Pages: 3511–3516
- Publisher: IEEE
- DOI: 10.1109/cdc.2010.5717274
BibTeX
@inproceedings{Jeltsema_2010,
title={{Mechanical memory elements: Modeling of systems with position-dependent mass revisited}},
DOI={10.1109/cdc.2010.5717274},
booktitle={{49th IEEE Conference on Decision and Control (CDC)}},
publisher={IEEE},
author={Jeltsema, Dimitri and Doria-Cerezo, Arnau},
year={2010},
pages={3511--3516}
}
References
- Pershin, Y. V. & Di Ventra, M. Experimental demonstration of associative memory with memristive neural networks. Neural Networks vol. 23 881–886 (2010) – 10.1016/j.neunet.2010.05.001
- 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
- Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. The missing memristor found. Nature vol. 453 80–83 (2008) – 10.1038/nature06932
- Stulov, A. Hysteretic model of the grand piano hammer felt. The Journal of the Acoustical Society of America vol. 97 2577–2585 (1995) – 10.1121/1.411912
- süße, Theoretische Grundlagen Der Elektrotechnik (0)
- van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
- Civelek, C. Mathematical modelling of rotational mechanical elements of higher order and their characteristics. Mathematical and Computer Modelling vol. 43 957–964 (2006) – 10.1016/j.mcm.2005.09.023
- Chua, L. O. & Szeto, E. W. High‐order non‐linear circuit elements: Circuit‐theoretic properties. International Journal of Circuit Theory and Applications vol. 11 187–206 (1983) – 10.1002/cta.4490110206
- 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
- Di Ventra, M., Pershin, Y. V. & Chua, L. O. Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors. Proceedings of the IEEE vol. 97 1717–1724 (2009) – 10.1109/jproc.2009.2021077
- Oster, G. F. & Auslander, D. M. The Memristor: A New Bond Graph Element. Journal of Dynamic Systems, Measurement, and Control vol. 94 249–252 (1972) – 10.1115/1.3426595
- Multidomain modeling of nonlinear networks and systems. IEEE Control Systems vol. 29 28–59 (2009) – 10.1109/mcs.2009.932927
- Chua, L. O. Nonlinear circuit foundations for nanodevices, part I: the four-element torus. Proceedings of the IEEE vol. 9 1830–1859 (2003) – 10.1109/jproc.2003.818319
- Chua, L. Memristor-The missing circuit element. IEEE Transactions on Circuit Theory vol. 18 507–519 (1971) – 10.1109/tct.1971.1083337
- Pershin, Y. V., La Fontaine, S. & Di Ventra, M. Memristive model of amoeba learning. Physical Review E vol. 80 (2009) – 10.1103/physreve.80.021926