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Interval Algorithms in Modeling of Multibody Systems

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Numerical Software with Result Verification

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2991))

Abstract

We will show how a variety of interval algorithms have found their use in the multibody modeling program MOBILE. This paper acquaints the reader with the key features of this open source software, describes how interval arithmetic help to implement new transmission elements, and reports on interval modeling of dynamics, which is an inherent part of multibody simulations. In the latter case, the interval extension of MOBILE enhanced with an interval initial value problem solver (based on VNODE) is presented. The functionality of this application is shown with some examples. We provide insights into techniques used to enhance already existing modeling software with interval arithmetic concepts.

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References

  1. Kecskeméthy, A.: Objektorientierte Modellierung der Dynamik von Mehrkörpersystemen mit Hilfe von "Ubertragungselementen. Fortschrittberichte VDI, Reihe 20 Nr. 88. VDI-Verlag, Düsseldorf (1993)

    Google Scholar 

  2. Kecskeméthy, A.: MOBILE Version 1.3. User’s guide (1999)

    Google Scholar 

  3. Knüppel, O.: PROFIL/BIAS—A Fast Interval Library. Computing 53, 277–287 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dyllong, E., Luther, W., Traczinski, H.: Modelling Geometric Objects and Tolerances with Intervals: Data Exchange with ISO Standard STEP. Presented at Validated Computing 2002 (May 2002) (submitted paper)

    Google Scholar 

  5. Schiehlen, W. (ed.): Multibody Systems Handbook. Springer, Berlin (1990)

    MATH  Google Scholar 

  6. Orlandea, N.: ADAMS (Theory and applications). In: DePater, A.D., Pacejka, H.B. (eds.) Proc. 3rd Seminar on Advanced Vehicle Systems Dynamics, Amalfi, Mai 1986, pp. 121–166 (1987)

    Google Scholar 

  7. Rosenthal, D.: Order n formulation for equations of motion of multibody systems. In: SDIO/NASA Workshop on Multibody Simulations, September 3, pp. 1122–1150 (1987)

    Google Scholar 

  8. Brandl, H., Johanni, R., Otter, M.: A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix. In: IFAC/IFIP/IMACS Symposium on Robotics, Wien (December 1986)

    Google Scholar 

  9. Featherstone, R.: Robot Dynamics Algorithms. Kluwer Academic Publishers, Boston (1987)

    Google Scholar 

  10. Kreuzer, E., Schiehlen, W.: NEWEUL — Software for the generation of symbolical equations of motion. In: Schiehlen [5], pp. 181–202

    Google Scholar 

  11. Wittenburg, J., Wolz, U.: The program MESA VERDE for robot dynamics. In: Proc. 3rd International Symposium of Robotic Research, Gonvieux (Chantilly), France (1985)

    Google Scholar 

  12. Wirfs-Brock, R., Wilkerson, B.: Object-oriented design: A responsibility-driven approach. In: OOPSLA 1989 Proceedings, October 1989, pp. 71–75 (1989)

    Google Scholar 

  13. Kecskeméthy, A.: Sparse-matrix generation of Jacobians for the object-oriented modelling of multibody dynamics. In: Pereira, M.S., Ambrósio, J.A.C. (eds.) Proceedings of the NATO-Advanced Study Institute on Computer Aided Analysis of Rigid and Flexible Mechanical Systems, Contributed Papers, Tróia, Portugal, June 27– July 9. vol. II, pp. 71–90 (1993)

    Google Scholar 

  14. American National Standards Institute / Institute of Electrical and Electronic Engineers, New York. IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Std. 754-1985 (1985)

    Google Scholar 

  15. Loh, E., Walster, G.W.: Rump’s Example Revisited. Reliable Computing 8(3), 245–248 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Krämer, W.: Die Berechnung von Standardfunktionen in Rechenanlagen. In: Chatterji, S.D., Fuchssteiner, B., Kulisch, U., Liedl, R., Purkert, W. (eds.) Jahrbuch Überblicke Mathematik 1992, pp. 97–115. Vieweg, Braunschweig (1992)

    Google Scholar 

  17. Alefeld, G., Herzberger, J.: Introduction to interval computations. Academic Press, New York (1983)

    MATH  Google Scholar 

  18. Krämer, W.: A Priori Worst Case Error Bounds for Floating-Point Computations. IEEE transactions on computers 47(7), 750–756 (1998)

    Article  Google Scholar 

  19. Luther, W., Traczinski, H.: Error propagation control in MOBILE : extended basic mathematical objects and kinetostatic transmission elements. In: Kecskeméthy, A., Schneider, M., Woernle, C. (eds.) Advances in Multibody Systems and Mechatronics, pp. 267–276. Institut für Mechanik und Getriebelehre, Technische Universität Graz, Graz (1999)

    Google Scholar 

  20. Hörsken, C., Traczinski, H.: Modeling of Multibody Systems with Interval Arithmetic. In: Krämer, W., Wolff von Gudenberg, J. (eds.) Scientific Computing, Validated Numerics, Interval Methods, pp. 317–328. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  21. Lohner, R.: Einschließung der Lösung gewönlicher Anfangs- und Randwertaufgaben und Anwendungen. PhD thesis, Universität Karlsruhe (1988)

    Google Scholar 

  22. Griewank, A.: Evaluating derivatives: principles and techniques of algorithmic differentiation. SIAM, Philadelphia (2000)

    MATH  Google Scholar 

  23. Stauning, O.: Automatic validation of numerical solutions. PhD thesis, Technical University of Denmark, Lyngby (1997)

    Google Scholar 

  24. Nedialkov, N.S.: The design and implementation of an object-oriented validated ODE solver. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  25. Lohner, R.: On the ubiquity of the wrapping effect in the computation of the error bounds. In: Kulisch, U., Lohner, R., Facius, A. (eds.) Perspectives on Enclosure Methods, pp. 201–217. Springer, New York (2001)

    Google Scholar 

  26. Bendsten, C., Stauning, O.: FADBAD, a flexible C++ package for automatic differentiation using the forward and backward methods. Technical Report 1996- x5-94, Technical University of Denmark, Lyngby (1996)

    Google Scholar 

  27. Bendsten, C., Stauning, O.: TADIFF, a flexible C++ package for automatic differentiation using Taylor series. Technical Report 1997-x5-94, Technical University of Denmark, Lyngby (1997)

    Google Scholar 

  28. Auer, E.: Ein verifizierender Anfangswertproblemlöser in C++ zur Integration in MOBILE. Master’s thesis, Gerhard Mercator Universität Duisburg (2002)

    Google Scholar 

  29. Berz, M., Makino, K.: Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliable Computing 4, 361–369 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  30. Hammer, R., Hocks, M., Kulish, U., Ratz, D.: Basic Algorithms (Basic numerical problems). In: Numerical toolbox for verified computing, Springer, Berlin (1995)

    Google Scholar 

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Authors and Affiliations

  1. Fakultät für Ingenieurwissenschaften, Universität Duisburg-Essen, 47048, Duisburg, Germany

    Ekaterina Auer, Andrés Kecskeméthy, Martin Tändl & Holger Traczinski

Authors
  1. Ekaterina Auer
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  2. Andrés Kecskeméthy
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  3. Martin Tändl
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  4. Holger Traczinski
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Editor information

Editors and Affiliations

  1. CNRS, UMR 7606, LIP6, University Pierre et Marie Curie, 4 place Jussieu, 75252, Paris cedex 05, France

    René Alt

  2. Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gauss-Straße 20, 42097, Wuppertal, Germany

    Andreas Frommer

  3. University of Louisiana at Lafayette,  

    R. Baker Kearfott

  4. Universität Duisburg-Essen, 47048, Duisburg, Germany

    Wolfram Luther

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© 2004 Springer-Verlag Berlin Heidelberg

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Auer, E., Kecskeméthy, A., Tändl, M., Traczinski, H. (2004). Interval Algorithms in Modeling of Multibody Systems. In: Alt, R., Frommer, A., Kearfott, R.B., Luther, W. (eds) Numerical Software with Result Verification. Lecture Notes in Computer Science, vol 2991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24738-8_8

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  • DOI: https://doi.org/10.1007/978-3-540-24738-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21260-7

  • Online ISBN: 978-3-540-24738-8

  • eBook Packages: Springer Book Archive

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