TY - JOUR
T1 - Solving mechanical systems with nonholonomic constraints by a Lie-group differential algebraic equations method
AU - Liu, Chein Shan
AU - Chen, Wen
AU - Liu, Li Wei
N1 - Funding Information:
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.
Publisher Copyright:
© 2017 American Society of Civil Engineers.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85021648132&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85021648132&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)EM.1943-7889.0001298
DO - 10.1061/(ASCE)EM.1943-7889.0001298
M3 - Article
AN - SCOPUS:85021648132
SN - 0733-9399
VL - 143
JO - Journal of Engineering Mechanics - ASCE
JF - Journal of Engineering Mechanics - ASCE
IS - 9
M1 - 04017097
ER -