Stability analysis of a simple rheonomic nonholonomic constrained system

doi:10.1088/1674-1056/25/12/124501

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.

Keywords: nonholonomic constrained system stabillity gradient system Lyapunov function

Received: 16 July 2016
Revised: 12 August 2016
Accepted manuscript online:

PACS:

45.20.Jj

(Lagrangian and Hamiltonian mechanics)

Fund:

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).

Corresponding Authors: Shi-Xing Liu
E-mail: liushixing@lnu.edu.cn

Cite this article:

Chang Liu(刘畅), Shi-Xing Liu(刘世兴), Feng-Xing Mei(梅凤翔) Stability analysis of a simple rheonomic nonholonomic constrained system 2016 Chin. Phys. B 25 124501

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