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Chen Xiangwei, Cao Qiupeng, Mei Fengxiang. GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 684-691. DOI: 10.6052/0459-1879-15-268
Citation: Chen Xiangwei, Cao Qiupeng, Mei Fengxiang. GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 684-691. DOI: 10.6052/0459-1879-15-268
shu

GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE

  • 1.

    Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China

  • 2. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China

  • 3. School of Aerospace, Beijing Institute of Technology, Beijing 100081, China

  • Received Date: July 19, 2015
  • Revised Date: January 03, 2016
    Graphical Abstract
    • Abstract
  • It is an important and di cult problem to study the stability of the non-steady and nonholonomic mechanical systems, and it is di cult to construct the Lyapunov function directly from the di erential equation. This paper gives an indirect method. The ten kinds of generalized gradient systems are proposed and the di erential equations of the ten kinds of generalized gradient systems are given respectively. Furthermore, the generalized gradient representations of a nonholonomic system of Chetaev's type are studied. The condition under which a nonholonomic system can be considered as a generalized gradient system is obtained, so the nonholonomic system of Chetaev's type is transformed into each generalized gradient systems. The characteristic of the generalized gradient systems can be used to study the stability of the nonholonomic system. This method appears to be more e ective when it is di cult to construct the Lyapunov function directly. Some examples are given to illustrate the application of the result.
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