Abstract
The object-oriented modeling language Dymola allows the physical modeling of large interconnected systems based on model components fromdifferent engineering domains. It generatessymbolic code for different target simulators. In this paper, a Dymola class library for the efficient generation of the equations of motion for multibody systems is presented. The library is based on aO(n) algorithm which is reformulated in an objectoriented way. This feature can also be interpreted as a bond graph oriented modeling of multibody systems. Furthermore a new algorithm for a certain class ofvariable structure multibody systems, such as systems with Coulomb friction, is presented, which allows the generation of efficient symbolic code.
Similar content being viewed by others
References
Brandl, H., Johanni, R., and Otter, M., ‘A very efficient algorithm for the simulation of robots and similar multibody-systems without inversion of the mass-matrix’, inTheory of Robots, selected papers from the IFAC/IFIP/IMACS Symposium, Vienna/Austria, December 1986, P. Kopacek, I. Troch, and K. Desoyer (eds.), Pergamon Press, 1988, pp. 95–100.
Brandl, H., Johanni, R., and Otter, M., ‘An algorithm for the simulation of multibody systems with kinematic loops’, inProceedings of the 7th World Congress on The Theory of Machines and Mechanisms, Pergamon Press, 1987, pp. 407–411.
Brooks, B. A. and Cellier, F. E., ‘Modeling of a distillation column using bond graphs’, inProceedings of the SCS International Conference on Bond Graph Modeling, San Diego, California, January 17–20, 1993, pp. 315–320.
Cellier, F. E.,Continuous System Modeling, Springer-Verlag, New York, 1991.
Cellier, F. E. and Elmqvist, H., ‘Automated formula manipulation supports object-oriented continuous-system modeling’,IEEE Control System Magazine 13(2), 1993, 28–38.
Elmqvist, H., ‘A structured model language for large continuous systems’, Ph.D. Dissertation, Report CODEN:LUTFD2/(TFRT-1015), Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, 1978.
Elmqvist, H., Åström, K. J., Schönthal, T., and Wittenmark, B.,Simnon — User's Guide for MS-DOS Computers, SSPA Systems, Gothenburg, Sweden, 1990.
Elmqvist, H.,Dymola — User's Manual, Dynasim AB, Research Park Ideon, Lund, Sweden, 1994.
Elmqvist, H., Cellier, F. E., and Otter, M., ‘Object-oriented modeling of hybrid systems’, inProceedings ESS'93, European Simulation Symposium, Delft, The Netherlands, October 1993, pp. xxxi-xli.
Elmqvist, H. and Otter, M., ‘Methods for tearing systems of equations in object-oriented modeling’, inProceedings ESM'94, European Simulation Multiconference, Barcelona, Spain, June 1994.
Franke, J. and Otter, M., ‘The Manutec r3 benchmark models for the dynamic simulation of robots’, Technical Report TR R101-93, Institute for Robotics and System Dynamics, DLR Oberpfaffenhofen, March 1993.
Glocker, C. and Pfeiffer, F., ‘Complementary problems in multibody systems with planar friction’, accepted for publication inApplied Mechanics (to appear).
Haug, E. J., Wu, S. C., and Yang, S. M., ‘Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion — Part I, Theory’,Mechanism and Machine Theory 21, 1986, 401–506.
Hild, D. R. and Cellier, F. E., ‘Object-oriented electronic circuit modeling using Dymola’, inProceedings OOS'94, SCS Object Oriented Simulation Conference, Tempe, Arizona, January 1994, pp. 68–75.
Hiller, M., Kecskeméthy, A., and Stelzle, W., ‘Ein Vergleich rekursiver Verfahren’, Internal Report, Universität Duisburg, Fachgebiet Mechatronik & Mechanik. A short version of this paper appeared in: Stelzle, W., ‘Ein Vergleich rekursiver Verfahren zur Untersuchung der Dynamik baumstrukturierter Mehrkörpersystem’,ZAMM 73, 1993, 107–109.
Karnopp, D. C., Margolis, D. L., and Rosenberg, R. C.,System Dynamics: A Unified Approach, 2nd ed., John Wiley, New York, 1990.
Korn, G. A.,Interactive Dynamic-System Simulation, McGraw-Hill, 1989.
Lötstedt, P., ‘Coulomb friction in two-dimensional rigid body systems’,ZAMM 61, 1981, 605–615.
Luh, J. Y. S., Walker, M. W., and Paul, R. P. C., ‘On-line computational scheme for mechanical manipulators’,Transactions of the ASME — Journal of Dynamic Systems Measurement and Control 102, 1980, 69–76.
Matchworks, Inc.,SIMULINK — User's Manual, South Natick, Mass., 1992.
Matsson, S. E. and Söderlind, G., ‘A new technique for solving high-index differential-algebraic equations using dummy derivatives’, inProceedings of the IEEE Symposium on Computer-Aided Control System Design, CACSD'92, Napa, California, March 1992.
Mitchell, E. E. L. and Gauthier, J. S.,ACSL: Advanced Continuous Simulation Language — Reference Manual, Edition 10.0, MGS, Concord., Mass., 1991.
Nagel, L. W., ‘Spice2: A computer program to simulate semiconductor circuits’, Berkeley, University of California, Electronic Research Laboratory, ERL-M520, 1975.
Otter, M., ‘DSblock: A neutral description of dynamic systems. Version 3.2’, Technical Report TR R81-92, Institute for Robotics and System Dynamics, DLR Oberpfaffenhofen, May 1992.
Otter, M., Hocke, M., Daberkow, A., and Leister, G., ‘An object-oriented data model for multibody systems’, inAdvanced Multibody System Dynamics, W. Schiehlen (ed.), Kluwer, 1993, pp. 19–58.
Otter, M., Objektorientierte Modellierung mechatronischer Systeme am Beispiel geregelter Robotor’, Dr.-Ing. Dissertation, Fortschrittberichte VDI, Reihe 20, No. 147, VDI-Verlag, 1995.
Pantelides, C. C., ‘The consistent initialization of differential-algebraic systems’,SIAM Journal of Scientific and Statistical Computing 9, 1988, 213–231.
Pfeiffer, F., ‘Über unstetige, insbesondere stoßerregte Schwingungen’,Zeitschrift für Flugwissenschaft und Weltraumforschung 12, 1988, 358–367.
Roberson, R. E. and Schwertassek, R.,Dynamics of Multibody Systems, Springer-Verlag, 1988.
Tarjan, R. E., ‘Depth first search and linear graph algorithms’,SIAM Journal of Scientific and Statistical Computing 1, 1972, 146–160.
Walker, M. and Orin, D., ‘Efficient dynamic computer simulation of robotic mechanisms’,ASME, Journal of Dynamic Systems, Measurement and Control 104, 1982, 205–211.
Wehage, R. A., ‘Application of matrix partitioning and recursive projection to order n solution of constrained equations of motion’, inProceedings of the 20th Biennial ASME Mechanisms Conference, Orlando, Florida, 1988.
Weiner, M. and Cellier, F. E., ‘Modeling and simulation of a solar energy system by use of bond graphs’, inProceedings SCS International Conference on Bond Graph Modeling, San Diego, California, January 17–20, 1993, pp. 301–306.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Otter, M., Elmqvist, H. & Cellier, F.E. Modeling of multibody systems with the object-oriented modeling language Dymola. Nonlinear Dyn 9, 91–112 (1996). https://doi.org/10.1007/BF01833295
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01833295