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Construction of Lyapunov Function for Dissipative Gyroscopic System |
| XU Wei1, YUAN Bo2, AO Ping1,3**
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1Shanghai Center for Systems Biomedicine, Key Laboratory of Systems Biomedicine of Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240
2Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240
3Department of Physics, Shanghai Jiao Tong University, Shanghai 200240
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| Cite this article: |
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XU Wei, YUAN Bo, AO Ping 2011 Chin. Phys. Lett. 28 050201 |
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Abstract We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems. Such a potential function serves as the corresponding Lyapunov function for the dynamics, hence it gives both quantitative and qualitative descriptions for stability of motion. As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system. We explicitly obtain the potential function for all parameter regimes in the linear limit, including those regimes where the Lyapunov function was previously believed not to exist.
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02.30.Yy
87.18.Vf
45.20.Jj
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Received: 28 September 2010
Published: 26 April 2011
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