Stability analysis of a simple rheonomic nonholonomic constrained system

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...

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Bibliographic Details
Published inChinese physics B Vol. 25; no. 12; pp. 314 - 317
Main Author 刘畅 刘世兴 梅凤翔
Format Journal Article
LanguageEnglish
Published 01.12.2016
Subjects
Lyapunov函数
梯度系统
稳定性分析
稳定性问题
运动微分方程
非完整力学系统
非完整系统
非完整约束系统
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Summary: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.
Bibliography:nonholonomic constrained system, stabillity, gradient system, Lyapunov function
Chang Liu, Shi-Xing Liu, and Feng-Xing Mei（ 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）
11-5639/O4
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.
ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/25/12/124501