Generalized Coordinate Partitioning Methods for Numerical Integration of Differential-Algebraic Equations of Dynamics
Explicit and implicit, stiffly stable numerical integration algorithms based on generalized coordinate partitioning are developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, backward differentiation formulas are applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of a numerical example.
KeywordsMultibody System Newton Iteration Differentiation Formula Algebraic Constraint Multibody Dynamic System
Unable to display preview. Download preview PDF.
- 1.ADAMS users’ guide: Mechanical Dynamics, Inc., 555 South Forest, Ann Arbor, Mich: USA 1981.Google Scholar
- 2.DADS users’ manual: Rev. 4.0, Computer Aided Design Software, Inc., Oakdale, Iowa: USA 1987.Google Scholar
- 4.Wittenburg, J.: Dynamics of systems of rigid bodies B.G. Teubner: Stuttgart, 1977.Google Scholar
- 5.Wittenburg, J., and Wolz, U.: Mesa Verde: A symbolic program for nonlinear articulated rigid body dynamics: ASME: Paper No. 85-DET-141 1985.Google Scholar
- 6.Bae, D.S., Hwang, R.S., and Haug, E.J.: A recursive formulation for real-time dynamic simulation: Advances in Design Automation ASME: New York, NY, USA pp. 499–508 1988.Google Scholar
- 7.Hwang, R.S., Bae, D.S., Haug, E.J., and Kuhl, J.G.: Parallel processing for real-time dynamic system simulation: Advances in Design Automation ASME: New York, NY, USA pp. 509–518 1988.Google Scholar
- 14.Brenan, K.E., Campbell, S.L., and Petzold, L.R.: Numerical solution of initial-value problems in differential-algebraic equations North-Holland: New York, NY, USA 1989.Google Scholar
- 15.Fuhrer, C.: On the description of constrained mechanical systems by differential/algebraic equations German Aerospace Research Establishment ( DFVLR ): Institute for Flight System Dynamics: 1987.Google Scholar
- 16.Chace, M.A.: Methods and experience in computer aided design of large-displacement mechanical systems: (E.J. Haug, ed.). NATO ASI: Vol. F9: Computer Aided Analysis and Optimization of Mechanical System Dynamics, Berlin-Heidelberg: Springer- Verlag 1984.Google Scholar
- 19.Haug, E.J.: Computer aided kinematics and dynamics of mechanical systems, Vol I: basic methods: Allyn and Bacon: Boston, MA USA 1989.Google Scholar
- 20.Strang, G.: Linear algebra and its applications, 2nd ed.: Academic Press: New York, NY USA 1980.Google Scholar
- 21.Gear, G.W.: Numerical initial value problems in ordinary differential equations: Prentice-Hall: New York, NY USA 1969.Google Scholar