中国物理B ›› 2016, Vol. 25 ›› Issue (12): 124501-124501.doi: 10.1088/1674-1056/25/12/124501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Stability analysis of a simple rheonomic nonholonomic constrained system

Chang Liu(刘畅), Shi-Xing Liu(刘世兴), Feng-Xing Mei(梅凤翔)   

  1. 1. College of Physics, Liaoning University, Shenyang 110036, China;
    2. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;
    3. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2016-07-16 修回日期:2016-08-12 出版日期:2016-12-05 发布日期:2016-12-05
  • 通讯作者: Shi-Xing Liu E-mail:liushixing@lnu.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11272050, 11202090, 11472124, 11572034, and 11572145), the Science and Technology Research Project of Liaoning Province, China (Grant No. L2013005), China Postdoctoral Science Foundation (Grant No. 2014M560203), and the Doctor Start-up Fund in Liaoning Province of China (Grant No. 20141050).

Stability analysis of a simple rheonomic nonholonomic constrained system

Chang Liu(刘畅)1,2, Shi-Xing Liu(刘世兴)1, Feng-Xing Mei(梅凤翔)3   

  1. 1. College of Physics, Liaoning University, Shenyang 110036, China;
    2. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China;
    3. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
  • Received:2016-07-16 Revised:2016-08-12 Online:2016-12-05 Published:2016-12-05
  • Contact: Shi-Xing Liu E-mail:liushixing@lnu.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11272050, 11202090, 11472124, 11572034, and 11572145), the Science and Technology Research Project of Liaoning Province, China (Grant No. L2013005), China Postdoctoral Science Foundation (Grant No. 2014M560203), and the Doctor Start-up Fund in Liaoning Province of China (Grant No. 20141050).

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摘要：

It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems.

关键词: nonholonomic constrained system, stabillity, gradient system, Lyapunov function

Abstract:

It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems.

Key words: nonholonomic constrained system, stabillity, gradient system, Lyapunov function

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj