Review of Classical Approaches for Constraint Enforcement in Multibody SystemsSource: Journal of Computational and Nonlinear Dynamics:;2008:;volume( 003 ):;issue: 001::page 11004DOI: 10.1115/1.2803257Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: 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.
keyword(s): Equations , Multibody systems , Differential equations AND Equations of motion ,
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contributor author | André Laulusa | |
contributor author | Olivier A. Bauchau | |
date accessioned | 2017-05-09T00:27:12Z | |
date available | 2017-05-09T00:27:12Z | |
date copyright | January, 2008 | |
date issued | 2008 | |
identifier issn | 1555-1415 | |
identifier other | JCNDDM-25643#011004_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/137576 | |
description abstract | 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. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Review of Classical Approaches for Constraint Enforcement in Multibody Systems | |
type | Journal Paper | |
journal volume | 3 | |
journal issue | 1 | |
journal title | Journal of Computational and Nonlinear Dynamics | |
identifier doi | 10.1115/1.2803257 | |
journal fristpage | 11004 | |
identifier eissn | 1555-1423 | |
keywords | Equations | |
keywords | Multibody systems | |
keywords | Differential equations AND Equations of motion | |
tree | Journal of Computational and Nonlinear Dynamics:;2008:;volume( 003 ):;issue: 001 | |
contenttype | Fulltext |