| 相对论性Birkhoff系统的Lie对称性和守恒量 |
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| 引用本文： | 傅景礼,王新民.相对论性Birkhoff系统的Lie对称性和守恒量[J].物理学报,2000,49(6):1023-1027. |
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| 作者姓名： | 傅景礼 王新民 |
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| 作者单位： | 商丘师范学院物理系，商丘 476000 |
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| 基金项目： | 国家自然科学基金(批准号：19972010)和河南省自然科学基金(批准号：984053100)资助的课题. |
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| 摘 要： | 给出相对论性Birkhoff系统的Pfaff-Birkhoff原理和Birkhoff方程.由微分方程在无限小变换下的不变性，定义相对论性Birkhoff系统无限小变换生成元，建立Lie对称的确定方程，得到结构方程和守恒量.并研究该系统的Lie对称性逆问题.给出实例以说明结果的应用.
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| 关 键 词： | 相对论性Birkhoff系统 Lie对称性 守恒量 |
| 收稿时间： | 1999-08-15 |
LIE SYMMETRIES AND CONSERVED QUANTITIES OF RELATIVISTIC BIRKHOFF SYSTEMS |
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| FU JING-LI and WANG XIN-MIN.LIE SYMMETRIES AND CONSERVED QUANTITIES OF RELATIVISTIC BIRKHOFF SYSTEMS[J].Acta Physica Sinica,2000,49(6):1023-1027. |
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| Authors: | FU JING-LI and WANG XIN-MIN |
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| Abstract: | The Pfaff-Birkhoff principle and the Birkhoff equations for relativistic Birkhoff systems are given. The definition of an infinitesimal generator for the relativistic Birkhoff systems is given; by using the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the systems are established; the structure equation and the conserved quantities are obtained. And the inverse problem of Lie symmetries of the systems is also studied. Two examples are given to illustrate the application of the result. |
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