Influence of Double Parameters on the Equilibrium Stability of Generalized Hamilton Systems

CHEN Xiang-wei; LI Yan-min; MEI Feng-xiang

doi:10.3879/j.issn.1000-0887.2014.12.011

Volume 35 Issue 12

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CHEN Xiang-wei, LI Yan-min, MEI Feng-xiang. Influence of Double Parameters on the Equilibrium Stability of Generalized Hamilton Systems[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1392-1397. doi: 10.3879/j.issn.1000-0887.2014.12.011

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Influence of Double Parameters on the Equilibrium Stability of Generalized Hamilton Systems

doi: 10.3879/j.issn.1000-0887.2014.12.011

¹School of Physics and Electrical Infornation, Shangqiu Normal University, Shangqiu, Henan 476000, P.R.China;²School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, P.R.China

Funds: The National Natural Science Foundation of China(11372169;10932002;11272050)

Received Date: 2014-07-28
Rev Recd Date: 2014-09-16
Publish Date: 2014-12-15

Abstract

Abstract

Influence of double parameters on the equilibrium stability of generalized Hamilton systems with additional terms was studied. Firstly, a generalized Hamilton system with additional terms was considered as a gradient system under certain conditions. Secondly, the characteristics of the gradient system was used to study the equilibrium stability and its dependance on the two parameters of the system. Thirdly, the stability domain was given in the parameter plane. The results show that the equilibrium of the system is likely to be stable, or asymptotically stable, or even unstable with the change of the two parameters, and the range of parameters corresponding to each equilibrium state is given.
- generalized Hamilton system,
- gradient system,
- stability,
- parameter plane

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References(17)

References

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