Advertisement

Dynamic Analysis. Equations of Motion

  • Javier García de Jalón
  • Eduardo Bayo
Part of the Mechanical Engineering Series book series (MES)

Abstract

This chapter deals with the direct dynamic problem which consists of determining the motion of a multibody system that results from the application of the external forces and/or the kinematically controlled or driven degrees of freedom. The direct dynamic analysis is also commonly referred to as the dynamic simulation. Its importance is steadily increasing in fields such as: automobile industry, aerospace, robotics, machinery, biomechanics, and others. The possibility of kinematically controlling some degrees of freedom in a dynamic problem has many practical applications. For example, in the analysis of vehicle suspensions, if the wheel is rigid, its center follows the trajectory determined by the rolling surface. The dynamic problem will determine the resulting motion of all the vehicle’s remaining elements.

Keywords

Constraint Equation Multibody System Base Body Canonical Equation Penalty Formulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bae, D.S. and Won, Y.S., “A Hamiltonian Equation of Motion for Real-time Vehicle Simulation”, Advances in Design and Automation 1990, Vol. 2, pp. 151–157, ASME Press, (1990).Google Scholar
  2. Bae, D.S. and Yang, S.M., “A Stabilization Method for Kinematic and Kinetic Constraint Equations”, Real-Time Integration Methods for Mechanical System Simulation, NATO ASI Series, Vol. 69, pp. 209–232, Springer-Verlag, (1990).Google Scholar
  3. Baumgarte, J., “Stabilization of Constraints and Integrals of Motion in Dynamical Systems”, Computer Methods in Applied Mechanics and Engineering, Vol. 1, pp. 1–16, (1972).MathSciNetADSMATHCrossRefGoogle Scholar
  4. Bayo, E., García de Jalón, J., and Serna, M.A., “A Modified Lagrangian Formulation for the Dynamic Analysis of Constrained Mechanical Systems”, Computer Methods in Applied Mechanics and Engineering, Vol. 71, pp. 183–195, (1988).MathSciNetADSMATHCrossRefGoogle Scholar
  5. Bayo, E., García de Jalón, J., Avello, A., and Cuadrado, J., “An Efficient Computational Method for Real Time Multibody Dynamic Simulation in Fully Cartesian Coordinates”, Computer Methods in Applied Mechanics and Engineering, Vol. 92, pp. 377–395, (1991).ADSMATHCrossRefGoogle Scholar
  6. Bayo, E. and Avello, A., “Singularity Free Augmented Lagrangian Algorithms for Constraint Multibody Dynamics”, to appear in the Journal of Nonlinear Dynamics, (1993).Google Scholar
  7. Brenan, K.E, Campbell, S.L., and Petzold, L.R., The Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, Elsevier Science Publishing, (1989).Google Scholar
  8. Chang, C.O. and Nikravesh, P.E., “An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems”, ASME Journal of Mechanisms, Transmissions and Automation in Design, Vol. 107, pp. 488–492, (1985).CrossRefGoogle Scholar
  9. García de Jalón, J., Avello, A., Jiménez, J.M., Martín, F., and Cuadrado, J., “Real Time Simulation of Complex 3-D Multibody Systems with Realistic Graphics”, Real-Time Integration Methods for Mechanical System Simulation, NATO ASI Series, Vol. 69, pp. 265–292, Springer-Verlag, (1990).Google Scholar
  10. Gear, C.W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, (1971).MATHGoogle Scholar
  11. Goldstein H., Classical Mechanics, 2nd edition, Addison-Wesley, (1980).MATHGoogle Scholar
  12. Haug, E.J., Computer—Aided Kinematics and Dynamics of Mechanical Systems, Volume I: Basic Methods, Allyn and Bacon, (1989).Google Scholar
  13. Jerkovsky, W., “The Structure of Multibody Dynamic Equations”, Journal of Guidance and Control, Vol. 1, pp. 173–182, (1978).MATHCrossRefGoogle Scholar
  14. Kamman, J.W. and Huston, R.L., “Dynamics of Constrained Multibody Systems”, ASME Journal of Applied Mechanics, Vol. 51, pp. 899–903, (1984).ADSMATHCrossRefGoogle Scholar
  15. Kim, S.S. and Vanderploeg, M.J., “A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations”, ASME Journal of Mechanisms, Transmissions and Automation in Design, Vol. 108, pp. 176–182, (1986a).CrossRefGoogle Scholar
  16. Kim, S.S. and Vanderploeg, M.J., “QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems”, ASME Journal on Mechanisms, Transmissions and Automation in Design, Vol. 108, pp. 183–188, (1986b).CrossRefGoogle Scholar
  17. Kurdila, A. J. and Narcowich F.J., “Sufficient Conditions for Penalty Formulation Methods in Analytical Dynamics”, to appear in Computational Mechanics, (1993).Google Scholar
  18. Lankarani, H.M. and Nikravesh, P.E., “Application of the Canonical Equations of Motion in Problems of Constrained Multibody Systems with Intermittent Motion”, Advances in Design Automation 1988, DE-Vol. 14, pp. 417–423, edited by S.S. Rao, ASME Press, (1988).Google Scholar
  19. Mani, N.K., Haug, E.J., and Atkinson, K.E., “Application of Singular Value Decomposition for Analysis of Mechanical System Dynamics”, ASME Journal on Mechanisms, Transmissions and Automation in Design, Vol. 107, pp. 82–87, (1985).CrossRefGoogle Scholar
  20. Nikravesh, P.E., “Some Methods for Dynamic Analysis of Constrained Mechanical Systems: A Survey”, Computer-Aided Analysis and Optimization of Mechanical System Dynamics, ed. by E.J. Haug, Springer-Verlag, pp. 351–368, (1984).Google Scholar
  21. Nikravesh, P.E. and Gim, G., “Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops”, Advances in Design Automation 1989, Vol. 3, pp. 27–33, ASME Press, (1989).Google Scholar
  22. Oden, J.T., Finite Elements. A Second Course, Volume II, Chapter 3, Prentice-Hall, (1983).Google Scholar
  23. Park, T.W. and Haug, E.J., “A Hybrid Numerical Integration Method for Machine Dynamic Simulation”, ASME Journal of Mechanisms, Transmissions and Automation in Design, Vol. 108, pp. 211–216, (1986).CrossRefGoogle Scholar
  24. Pars, L.A., A Treatise of Analytical Dynamics, William Heineman Ltd., (1965).Google Scholar
  25. Paul, B., “Analytical Dynamics of Mechanisms — A Computer-Oriented Overview”, Mechanism and Machine Theory, Vol. 10, pp. 481–507, (1975).CrossRefGoogle Scholar
  26. Serna, M.A., Aviles, R., and García de Jalón, J., “Dynamic Analysis of Planar Mechanisms with Lower-Pairs in Basic Coordinates”, Mechanism and Machine Theory, Vol. 17, pp. 397–403, (1982).CrossRefGoogle Scholar
  27. Shampine, L. and Gordon, M., Computer Solution of ODE. The Initial Value Problem, Freeman, (1975).Google Scholar
  28. Steigerwald, M.F., “BDF Methods for DAEs in Multibody Dynamics: Shortcomings and Improvements”, in Real-Time Integration Methods for Mechanical System Simulation, NATO ASI Series, Vol. 69, pp. 345–352, Springer-Verlag, (1990).Google Scholar
  29. Unda, J., García de Jalón, J., Losantes, F., and Enparantza, R., “A Comparative Study of Some Different Formulations of the Dynamic Equations of Constrained Mechanical Systems”, ASME Journal of Mechanisms, Transmissions and Automation in Design, Vol. 109, pp. 466–474, (1987).CrossRefGoogle Scholar
  30. Vanderplaats, G.N., Numerical Optimization Techniques for Engineering Design: with Applications, McGraw-Hill, (1984).MATHGoogle Scholar
  31. Wehage, R.A. and Haug, E.J., “Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems”, ASME Journal of Mechanical Design, Vol. 104, pp. 247–255, (1982).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Javier García de Jalón
    • 1
  • Eduardo Bayo
    • 2
  1. 1.Department of Applied MechanicsUniversity of Navarra and CEITDonostia - San SebastianSpain
  2. 2.Department of Mechanical EngineeringUniversity of California, Santa BarbaraSanta BarbaraUSA

Personalised recommendations