Solving Mechanical Systems with Nonholonomic Constraints by a Lie-Group Differential Algebraic Equations Method
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
A Lie-group differential algebraic equations (LGDAE) method, which is developed for solving differential-algebraic equations, is a simple and effective algorithm based on the Lie group and the Newton iterative scheme. This paper deepens the theoretical foundation of the LGDAE method and widens its practical applications to solve nonlinear mechanical systems with nonholonomic constraints. After obtaining the closed-form formulation of elements of a one-parameter group and refining the algorithm of the LGDAE method, this differential-algebraic split method is applied to solve nine problems of nonholonomic mechanics in order to evaluate its accuracy and efficiency. Numerical computations of the LGDAE method exhibit the preservation of the nonholonomic constraints with an error smaller than . Comparing the closed-form solutions demonstrates that the numerical results obtained are highly accurate, indicating that the present scheme is promising.
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Acknowledgments
The authors thank anonymous referees who gave constructive comments that enriched the content of the paper. This research was supported by the projects NSC-102-2221-E-002-125-MY3 and MOST 104-2218-E-002-026-MY3 from the Ministry of Science and Technology of Taiwan. The 1000 Talents Plan of China with A1211010 and the Chair Professor of Hohai University granted to the first author are highly appreciated.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Nov 4, 2016
Accepted: Feb 28, 2017
Published online: Jun 29, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 29, 2017
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