Stability analysis of a simple rheonomic nonholonomic constrained system  

作　　者：刘畅 刘世兴 梅凤翔 

机构地区：[1]College of Physics,Liaoning University [2]State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology [3]School of Aerospace Engineering,Beijing Institute of Technology

出　　处：《Chinese Physics B》2016年第12期314-317,共4页中国物理B（英文版）

基　　金：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);the Doctor Start-up Fund in Liaoning Province of China(Grant No.20141050)

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.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 

分 类 号：O175[理学—数学]