Collocation Methods for the Investigation of Periodic Motions of Constrained Multibody Systems

Multibody System Dynamics

Volumn 5, Issue 2, 2001, Pages 133-158

  Franke, C ^a   Fuhrer C ^b  

^a UNIVERSITY OF ULM   (Germany)

^b LUND UNIVERSITY   (Sweden)

Author keywords

Collocation; Constrained multibody systems; Differential algebraic equations; Floquet multipliers; Periodic motions; Stability analysis

Indexed keywords

EID: 18044401655     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009862617209     Document Type: Article

References (31)

1. Allgower, E.L. and Georg, K., Numerical Continuation Methods, Springer-Verlag, Berlin, 1990.
2. Arnold, M., Zur Theorie und zur numerischen Lösung von Anfangswertproblemen für differentiell-algebraische Systeme von höherem Index, Rechnerunterstütze Verfahren, Vol. 20, No. 264, VDI-Verlag, Düsseldorf, 1998.
3. Ascher, U.M., Mattheij, R.M.M. and Russell, R.D., Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1988.
4. Ascher, U.M. and Petzold, L.R., 'Projected implicit Runge-Kutta methods for differentialalgebraic equations', SIAM J. Numer. Anal. 28(4), 1991, 1097-1120.
5. Ascher, U.M. and Petzold, L.R., 'Projected collocation for higher-order higher-index differential-algebraic equations', J. Comput. Appl. Math. 43, 1992, 243-259.
6. Ascher, U.M. and Petzold, L.R., 'Stability of computational methods for constrained dynamical systems', SIAM J. Sci. Statist. Comput. 14(1), 1993, 95-120.
7. Ascher, U.M. and Spiteri, R.J., 'Collocation software for boundary value differential-algebraic equations', SIAM J. Sci. Stat. Comput. 15, 1994, 938-952.
8. Brenan, K.E., Campbell, S.L. and Petzold, L.R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
9. Doedel, E.J., Keller, H.B. and Kernevez, J.P., 'Numerical analysis and control of bifurcation problems', Internat. J. Bifurcation and Chaos 1, 1991, 745-772. (II) Bifurcation in infinite dimensions.
10. Eich-Soellner, E. and Führer, C., Numerical Methods in Multibody Dynamics, Teubner, Stuttgart, 1998.
11. Farkas, M., Periodic Motions, Springer-Verlag, New York, 1994.
12. Franke, C., Numerical Methods for the Investigation of Periodic Motions in Multibody System Dynamics: A Collocation Approach, Shaker Verlag, Aachen, 1998.
13. Gantmacher, F.R., Applications of the Theory of Matrices, Interscience Publishers, New York, 1959.
14. Hairer, E., Lubich, C. and Roche, M., The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics, Vol. 1409, Springer-Verlag, Berlin, 1989.
15. Hairer, E. and Wanner, G., Solving Ordinary Differential Equations II, second edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin, 1996.
16. Haug, E.J. and Yen, J., 'Implicit numerical integration of constrained equations of motion via generalized coordinate partitioning', J. Mech. Design 114(2), 1992, 296-304.
17. Kaas-Petersen, C., 'Chaos in a railway bogie', Acta Mech. 61, 1986, 89-107.
18. Knudsen, C., Feldberg, R. and Jaschinski, A., 'Non-linear dynamic phenomena in the behavior of a railway wheelset model', Nonlinear Dynam. 2, 1991, 389-404.
19. Lamour, R., 'Oscillations in differential-algebraic equations', Preprint 272, Humboldt Universität Berlin, Fachbereich Mathematik, 1991.
20. Lamour, R., März, R. and Winkler, R., 'How Floquet-theory applies to differential-algebraic equations', Preprint 96-15, Humboldt Universität Berlin, Institut für Mathematik, 1996.
21. Leister, G., 'Beschreibung und Simulation von Mehrkörpersystemen mit geschlossenen kinematischen Schleifen', Ph.D. Thesis, University Stuttgart, 1992. Also: VDI-Fortschrittsber. (11), 167, VDI-Verlag, Düsseldorf, 1992.
22. Leister, G., 'Beschreibung und Simulation von Mehrkörpersystemen mit geschlossenen kinematischen Schleifen', Ph.D. Thesis, University Stuttgart, 1992. Also: VDI-Fortschrittsber. (11), 167, VDI-Verlag, Düsseldorf, 1992.
23. Netter, H., 'Rad-Schiene-Systeme in differential-algebraischer Darstellung', Ph.D. Thesis, Technische Universität München, 1998. Also: VDI-Fortschrittsber. (12), 352, VDI-Verlag, Düsseldorf, 1998.
24. Netter, H., 'Rad-Schiene-Systeme in differential-algebraischer Darstellung', Ph.D. Thesis, Technische Universität München, 1998. Also: VDI-Fortschrittsber. (12), 352, VDI-Verlag, Düsseldorf, 1998.
25. Petzold, L.R., 'A description of DASSL: A differential/algebraic system solver', in Scientific Computing, R.S. Stepleman et al. (eds), North-Holland, Amsterdam, 1983, 65-68.
26. Seydel, R., 'A continuation algorithm with step control', in Numerical Methods for Bifurcation Problems, Proceedings of a Conference in Dortmund, 1983, T. Küpper, H.D. Mittelmann and H. Weber (eds), International Series of Numerical Mathematics, Vol. 70, Birkhäuser, Basel, 1984, 480-494.
27. Seydel, R., Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos, Springer-Verlag, New York, 1994.
28. Simeon, B., Führer, C. and Rentrop, P., 'The Drazin inverse in multibody dynamics', Numer. Math. 64, 1993, 521-539.
29. Simeon, B., Führer, C. and Rentrop, P., 'Wheelset', in Test Set for IVP Solvers, Centrum voor Wiskunde en Informatica, Amsterdam, 1995, http://www.cwi.nl/cwi/projects/IVPtestset.shtml.
30. True, H. and Jensen, J.C., 'Chaos and asymmetry in railway vehicle dynamics', Period. Polytech. Transp. Engrg. 22(1), 1994, 55-68.
31. Wehage, R.A. and Haug, E.J., 'Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems', J. Mech. Design 134, 1982, 247-255.