Stability analysis of a simple rheonomic nonholonomic constrained system |
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Affiliation: | 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 |
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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. |
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Keywords: | nonholonomic constrained system stabillity gradient system Lyapunov function |
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