Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Solving Mechanical Systems with Nonholonomic Constraints by a Lie-Group Differential Algebraic Equations Method
AbstractA 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 GL(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.
Solving Mechanical Systems with Nonholonomic Constraints by a Lie-Group Differential Algebraic Equations Method
AbstractA 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 GL(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.
Solving Mechanical Systems with Nonholonomic Constraints by a Lie-Group Differential Algebraic Equations Method
Liu, Chein-Shan (Autor:in) / Liu, Li-Wei / Chen, Wen
2017
Aufsatz (Zeitschrift)
Englisch
| British Library Online Contents | 2009
Methods for Solving Algebraic Equations and Their Systems
| Springer Verlag | 2009
Maslov dequantization and the homotopy method for solving systems of nonlinear algebraic equations
| British Library Online Contents | 2008