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| A discrete gradient integration method for generalized Hamilton systems |
| Revised:February 21, 2003 |
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| DOI：10.7511/jslx20045101 |
| KeyWord:discrete gradient,discrete gradient integration method,generalized Hamilton system,generalized Hamilton control system |
| Zhang Suying~1 Deng Zichen~ |
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| Abstract: |
| For generalized Hamilton system and generalized Hamilton control system, by Hamilton function based on energy and the discrete gradient method, the numerical solution method that can preserve Hamilton function properties of Hamilton system is given in the presented paper. Firstly, the generalized Hamilton system models and the energy change rates based on energy concept of the dynamic systems are established, then based on the definition of discrete gradient, the discrete gradient integration method is proposed and the proof of the integration algorithm precision is given. It is proved that the integration method of this paper can effectively preserve the rate of Hamilton function with respect to time. The numerical example shows that the method proposed in this paper is effective. The work of this paper will provide a new way for the further studies of Hamilton dynamic system. |
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