https://scholars.lib.ntu.edu.tw/handle/123456789/624861
標題: | Solving mechanical systems with nonholonomic constraints by a Lie-group differential algebraic equations method | 作者: | Liu C.-S Chen W Liu L.-W. LI-WEI LIU |
關鍵字: | Differential-algebraic equations; Lie group GLGL(n,R); Lie-group differential algebraic equations method.; Nonholonomic mechanics | 公開日期: | 2017 | 卷: | 143 | 期: | 9 | 來源出版物: | Journal of Engineering Mechanics | 摘要: | 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 GL(n,R) 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 GLGL(n,R) 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 10-10. Comparing the closed-form solutions demonstrates that the numerical results obtained are highly accurate, indicating that the present scheme is promising. © 2017 American Society of Civil Engineers. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85021648132&doi=10.1061%2f%28ASCE%29EM.1943-7889.0001298&partnerID=40&md5=6df02e1eae5c637be30273c45405200c https://scholars.lib.ntu.edu.tw/handle/123456789/624861 |
ISSN: | 07339399 | DOI: | 10.1061/(ASCE)EM.1943-7889.0001298 | SDG/關鍵字: | Differential equations; Iterative methods; Lie groups; Mechanics; Numerical methods; Closed form solutions; Differential algebraic; Differential algebraic equations; Non holonomic constraint; Non-holonomic mechanics; Nonlinear mechanical systems; Numerical computations; Theoretical foundations; Algebra; algorithm; engineering; equation; mechanics |
顯示於: | 土木工程學系 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。