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Research Papers

Review of Classical Approaches for Constraint Enforcement in Multibody Systems

[+] Author and Article Information
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 30332-0150

J. Comput. Nonlinear Dynam 3(1), 011004 (Nov 02, 2007) (8 pages) doi:10.1115/1.2803257 History: Received November 16, 2006; Revised June 18, 2007; Published November 02, 2007

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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Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Geometric representation of constraint dynamics with holonomic constraints. Although appearing as orthogonal projections in this illustration, projections, in fact, operate in the metric of the inverse of the mass matrix.

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