Geodesic
Implementation of computer model for the unilateral multibody systems dynamics
Matematičeskoe modelirovanie, Tome 18 (2006) no. 12, pp. 95-106.

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Computer modeling and simulation of dynamics for multibody systems consisting of rigid bodies with unilateral constraints (MBSUC) is not an easy problem. When developing the models, one encounters several obstacles difficult to overcome. In the current paper an approach to modeling the MBSUC dynamics based on Modelica language is described. First of all so called acausal modeling approach is applied here because MBSUC is represented in this case via the hybrid automata having a large number or even very large number of states. It turns out one can avoid the model structural complexity growth on this way, at least on the Modelica level of the description. The problem of the regularization for transitions between the states of the unilateral constraint is under resolution. The transitions being simulated are the following ones: between relative flight and contact, and for the case of contact between sliding and rolling. The model of dry friction is taken into account. Impacts distributed throughout the MBSUC are also implemented. The comprehensive verification of the regularized model in compare with the model of the exact hybrid automata is carried out. An example of the heavy ellipsoid on the rough plane is used for this purpose. The ellipsoid supposed to have a possibility of jumps, slipping, and rolling. Some known qualitative examples of the rigid body dynamics on the rough plane are also under consideration. 
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I. I. Kosenko. Implementation of computer model for  the unilateral multibody systems dynamics. Matematičeskoe modelirovanie, Tome 18 (2006) no. 12, pp. 95-106. http://geodesic.mathdoc.fr/item/MM_2006_18_12_a7/

[1] I. Vittenburg, Dinamika sistem tverdykh tel, Mir, M., 1980 | MR

[2] R. Sinha, C. J. J. Paredis, V-C. Liang, P. K. Khosla, “Modeling and simulation methods for design of engineering systems”, Journal of Computing and Information Science in Engineering, 1:1 (2001), 84–91 | DOI

[3] I. I. Kossenko, M. S. Stavrovskaia, “How one can simulate dynamics of rolling bodies via Dymola: approach to model multibody system dynamics using Modelica”, Proceedings of the 3rd InternationalModelica Conference (November 3–4, 2003, Linköpings Universitet, Linköping, Sweden), ed. Peter Fritzson, Linköpings Universitet, Linköping, 2003

[4] I. I. Kossenko, “Implementation of Unilateral Multibody Dynamics on Modelica”, Proceedings of the 4th International Modelica Conference (March 7–8, 2005, Hamburg University of Technology, Hamburg-Harburg, Germany), ed. Gerhard Schmitz, Hamburg University of Technology, Hamburg-Harburg, 2005

[5] Modelica – a unified object-oriented language for physical systems modeling, Tutorial, Modelica Association, 2000

[6] Modelica – a unified object-oriented language for physical systems modeling, Language specification, Modelica Association, 2004

[7] http://www.modelica.org

[8] Dymola. Dynamic modeling laboratory, User's manual. Version 5.3a, Dynasim AB, Research Park Ideon, Lund, 2004

[9] F. Pfaiffer, “Sistemy mnogikh tel s odnostoronnimi svyazyami”, PMM, 65:4 (2001), 681–687 | MR

[10] I. V. Novozhilov, Fraktsionnyi analiz, Izd-vo MGU, M., 1995

[11] E. Raus, Dinamika sistemy tverdykh tel, T. 1, Nauka, M., 1983

[12] A. P. Ivanov, Dinamika sistem s mekhanicheskimi soudareniyami, Mezhdunarodnaya programma obrazovaniya, M., 1997 | MR

[13] A. P. Markeev, Dinamika tela, soprikasayuschegosya s tverdoi poverkhnostyu, Nauka, M., 1992 | MR | Zbl