Summary
Different from the usual use of Kane's approach a description of mechanical systems in relative motion is presented in the paper. Kane's equations require determination of the absolute motion of the system with regard to an inertial reference frame. If one wants to apply these equations to a system moving relative to a noninertial reference frame, one still needs to determine the absolute motion of the system by summing up to the motion of the moving reference frame and the system's motion relative to this frame. Results of the paper permit a direct formulation of the equations of motion without the need to determine the absolute motion. This is achieved by adaptation of Kane's equations to relative motion, which is general and may be applied to any mechanical system in relative motion. We obtained our results for purposes of railway vehicle dynamics. Hence some material concerning automatic generation of the equations of motion for the systems of a railway vehicle type is included as an example of the application of our approach.
Similar content being viewed by others
References
Bonivert, L., Maes, P., Samin, J. C.: Simulation of the lateral dynamics of the GLT vehicle by means of ROBOTRAN; a Model Generator for Robots. In: Proc. Conf. on Simulation in Factory of the Future. Belgium: SCS Publications 1988.
Choromański, W., Zboiński, K.: The software package for automatic generation of equations of motion and vehicle dynamics analyses. In: X Scientific Conference Railway Vehicles—Dynamics, vol. 3, pp. 34–55, Wrocław, Poland 1994. Wrocław: Wrocław Tech. Univ. 1994 (in Polish).
Choromański, W., Zboiński, K.: The software package Ulysses for automatic generation of equations and simulation of vehicle motion. In: Proc. Sci. Conf. on Transport Systems Engineering-Technical Transport Means, sec. 4, pp. 47–52. Warsaw, Poland 1995. Warsaw: Warsaw Univ. of Tech. 1995.
Fisette, P., Samin, J. C.: Lateral dynamics of a light railway vehicle with independent wheels. In: The dynamics of Vehicles on Roads and on Tracks (Sauvage G. ed.), 12th IAVSD Symposium, Lyon, France 1991. Suppl. to Vehicle Systems Dynamics,20, 157–171 (1991).
Garg, V. K., Dukkipati, R. V.: Dynamics of railway vehicle systems. Canada: Academic Press 1984.
Huston, R.: Useful procedures in multibody dynamics. In: Proc. IUTAM/IFT MM Symposium Dynamics of Multibody Systems, (Bianchi, G., Schiehlen, W., eds.), pp. 69–77. Berlin Heidelberg: Springer 1986.
Huston, R., Passerello, C. E.: On multi-rigid body systems. Comp. and Struct.10, 439–446 (1979).
Huston, R., Passerello, C. E., Harlow, M. W.: Dynamics of multi-rigid body systems. ASME J. Appl. Mech.45 (4), 889–894 (1978).
Kane, T. R.: Dynamics of non-holonomic systems. ASME J. Appl. Mech.28, 574–578 (1961).
Kane, T. R., Levinson, D. A.: Dynamics: Theory and Applications. New York: McGraw-Hill 1985.
Kane, T. R., Levinson, D. A.: Formulation of equations of motion for complex spacecraft. J. Guid. Cont.3, (2), 99–112 (1980).
Kane, T. R., Likins, P. W., Levinson, D. A.: Spacecraft dynamics. New York: McGraw-Hill 1983.
Kortum, W., Sharp, R. S., de Pater, A. D.: Application of multibody computer codes to vehicle system dynamics. Progress Report on a Workshop and Resulting Activities-12th IAVSD Symposium. Oberpfaffenhofen: Society for Engineering and Scientific Education 1991.
Knothe, K. (ed.), Kisilowski, J. (ed.): Advanced railway vehicle systems dynamics. Warsaw: WNT 1991.
Krieg, M.: Equations of motion for holonomic and non-holonomic multibody systems. DIPL-4, University of Stuttgart, Institute B of Mechanics 1982 (in German).
Lurie, A. I.: Analytical mechanics. Moscow: FizMatGIz 1961 (in Russian).
Popp, K., Schiehlen, W.: Fahrzeugdynamik. Stuttgart: Teubner 1993.
Robertson, R. E.: Computer-oriented dynamic modelling of spacecraft: historical evaluation of Eulerian multibody formalism since 1750. In: 28th Int. Astronautical Conf., paper 77-A 11. Prague: IAF 1977.
Robertson, R. E., Wittenburg, J.: A dynamical formalism for an arbitrary number of interconnected rigid bodies with reference to the problem of satellite attitude control. In: Proc. 3rd IFAC Congr., pp. 46D.2–46D.9, London 1966.
Schaechter, D. B., Levinson, D. A.: Interactive computerized symbolic dynamics for the dynamicist. J. Astronaut. Sci.36, (4), 365–388 (1988).
Schiehlen, W., (ed.): Multibody systems handbook. Berlin: Springer 1990.
Wallrapp, O.: Elastic vehicle guideway structures. In: 3rd seminar on Advanced Vehicle System Dynamics (A. D. de Pater, H. B. Pacejka, eds.), pp. 215–232. Amfalti, Italy 1977. Amsterdam: Swets & Zeitlinger 1987.
Wallrapp, O., Jaschinski, A.: Dynamische Simulation mechanischer Systeme mit MEDYNA-ein Rechenprogramm zur Analyse und Auslegung: ZEV-Glassers Annalen.109, 463–469 (1985).
Wallrapp, O., Kortuem, W.: General purpose software for vehicle system dynamics using multibody formalism. In: Proc. 1st European Cars/Track Simulation Symp., (M. R. Heller, ed.). München: Control Data GmbH 1984.
Wittenburg, J.: Dynamics of systems of rigid bodies. Leitfaden der angewandten Mathematik und Mechanik, (H. Gortler, ed.), vol. 33. Stuttgart: Teubner 1977.
Zboiński, K.: Modelling and simulation of vehicle in curves-use of computer methods to modelling technique evaluation. In: X Scientific Conference Railway Vehicles-Dynamics, vol. 3, pp. 247–267, Wrocław, Poland 1994. Wrocław Wrocław Tech. Univ. 1994 (in Polish).
Zboiński, K.: The importance of imaginary forces and kinematic-type non-linearities for the description of railway vehicle dynamics. Proc. Inst. Mech. Eng. F-J. Rail and rapid Transit.213 (F4), 199–210 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zboiński, K. Relative kinematics exploited in Kane's approach to describe multibody systems in relative motion. Acta Mechanica 147, 19–34 (2001). https://doi.org/10.1007/BF01182349
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01182349