| 高维增广相空间中广义力学系统的Lie对称定理及其逆定理 |
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| 引用本文： | 乔永芬,起淑红.高维增广相空间中广义力学系统的Lie对称定理及其逆定理[J].商丘师范学院学报,2000,16(4):1-5. |
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| 作者姓名： | 乔永芬 起淑红 |
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| 作者单位： | 东北农业大学农工系!黑龙江哈尔滨150030 |
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| 基金项目： | 黑龙江省自然科学基金资助项目! (1 9950 7) |
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| 摘 要： | 给出高维增广相空间中广义力学系统的Ｌｉｅ对称定理及其逆定理，首先，分析运动微分方程在无限小变换下的不变性建立完整非保守广义力学系统Ｌｉｅ对称的确定方程。得到Ｌｉｅ对称的结构方程和守恒方程，其次，讨论了Ｌｉｅ对称的逆问题，最后举例说明结果的应用。
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| 关 键 词： | 高维增广相空间 Lie对称定理 广义力学系统 |
Lie's symmetrical theorem and its inverse of generalized mechanical systems in dimensional extended phase space |
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| QIAO Yong fen,ZHAO Shu hong.Lie's symmetrical theorem and its inverse of generalized mechanical systems in dimensional extended phase space[J].Journal of Shangqiu Teachers College,2000,16(4):1-5. |
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| Authors: | QIAO Yong fen ZHAO Shu hong |
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| Abstract: | In this paper,the Lie's symmetrical theorem and its inverse of generalized mechanical systems in dimensional extended phase space are given.Firstly,according to the invariance of differential equations of motion under the infinitesimal transformations,the determining equations of the Lie symmetry of the holonomic non conservative generalized mechanical systems are established.The Lie's symmetrical structural equation and conservative equations are obtained.Secondly,the inverse problem of the Lie symmetry is discussed.Finally,an example to illustrate the application of the result is given. |
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| Keywords: | dimensional extended phase space generalized mechanics Lie's symmetrical theorem conservative quantity |
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