A hallmark of multibody dynamics is that most formulations involve a number of constraints. Typically, when redundant generalized coordinates are used, equations of motion are simpler to derive but constraint equations are present. While the dynamic behavior of constrained systems is well understood, the numerical solution of the resulting equations, potentially of differential-algebraic nature, remains problematic. Many different approaches have been proposed over the years, all presenting advantages and drawbacks: The sheer number and variety of methods that have been proposed indicate the difficulty of the problem. A cursory survey of the literature reveals that the various methods fall within broad categories sharing common theoretical foundations. This paper summarizes the theoretical foundations to the enforcement in constraints in multibody dynamics problems. Next, methods based on the use of Lagrange’s equation of the first kind, which are index-3 differential-algebraic equations in the presence of holonomic constraints, are reviewed. Methods leading to a minimum set of equations are discussed; in view of the numerical difficulties associated with index-3 approaches, reduction to a minimum set is often performed, leading to a number of practical algorithms using methods developed for ordinary differential equations. The goal of this paper is to review the features of these methods, assess their accuracy and efficiency, underline the relationship among the methods, and recommend approaches that seem to perform better than others.
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January 2008
Research Papers
Review of Classical Approaches for Constraint Enforcement in Multibody Systems
André Laulusa,
André Laulusa
SIMUDEC Pte Ltd., Singapore Science Park II
, Singapore 117628, Singapore
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Olivier A. Bauchau
Olivier A. Bauchau
Daniel Guggenheim School of Aerospace Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332-0150
Search for other works by this author on:
André Laulusa
SIMUDEC Pte Ltd., Singapore Science Park II
, Singapore 117628, Singapore
Olivier A. Bauchau
Daniel Guggenheim School of Aerospace Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332-0150J. Comput. Nonlinear Dynam. Jan 2008, 3(1): 011004 (8 pages)
Published Online: November 2, 2007
Article history
Received:
November 16, 2006
Revised:
June 18, 2007
Published:
November 2, 2007
Citation
Laulusa, A., and Bauchau, O. A. (November 2, 2007). "Review of Classical Approaches for Constraint Enforcement in Multibody Systems." ASME. J. Comput. Nonlinear Dynam. January 2008; 3(1): 011004. https://doi.org/10.1115/1.2803257
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