Implicit Numerical Integration of Constrained Equations of Motion Via Generalized Coordinate Partitioning

[+] Author and Article Information
E. J. Haug, Jeng Yen

Center for Simulation and Design Optimization and Departments of Mechanical Engineering and Mathematics, The University of Iowa, Iowa City, IA 52242

J. Mech. Des 114(2), 296-304 (Jun 01, 1992) (9 pages) doi:10.1115/1.2916946 History: Received May 01, 1990; Online June 02, 2008


An implicit, stiffly stable numerical integration algorithm is 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 Formula (BDF) numerical integration algorithm is used to integrate 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 an example.

Copyright © 1992 by The American Society of Mechanical Engineers
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