Construction of Lyapunov Function for Dissipative Gyroscopic System
XU Wei1, YUAN Bo2, AO Ping1,3**
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
Construction of Lyapunov Function for Dissipative Gyroscopic System
XU Wei1, YUAN Bo2, AO Ping1,3**
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
摘要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.
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.
XU Wei;YUAN Bo;AO Ping;**
. Construction of Lyapunov Function for Dissipative Gyroscopic System[J]. 中国物理快报, 2011, 28(5): 50201-050201.
XU Wei, YUAN Bo, AO Ping, **
. Construction of Lyapunov Function for Dissipative Gyroscopic System. Chin. Phys. Lett., 2011, 28(5): 50201-050201.
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