Solving mechanical systems with nonholonomic constraints by a Lie-group differential algebraic equations method

Chein Shan Liu, Wen Chen, Li Wei Liu

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 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.

Original languageEnglish
Article number04017097
JournalJournal of Engineering Mechanics
Volume143
Issue number9
DOIs
Publication statusPublished - 2017 Sep 1

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering

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