| Lagrange函数等效变换对力学系统对称性和守恒量的影响 |
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| 引用本文： | 丁光涛.Lagrange函数等效变换对力学系统对称性和守恒量的影响[J].安徽师范大学学报(自然科学版),2009,32(1). |
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| 作者姓名： | 丁光涛 |
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| 作者单位： | 安徽师范大学,物理与电子信息学院,安徽,芜湖,241000 |
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| 摘 要： | 研究Lagrange函数两种等效变换对力学系统对称性和守恒量的影响.在规范等效变换下,系统的Noether守恒量保持不变,而Noether等式改变,给出了Noether对称性不变的条件.在同位等效变换下,系统的Noether守恒量仍保持不变,但Noether对称性改变,给出了构造新的对称变换的方法.在两种等效变换下,系统Lie对称性和Hojman守恒量保持不变.并举例说明结果的应用.
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| 关 键 词： | Lagrange函数的规范等效变换 Lagrange函数的同位等效变换 Noether对称性 Lie对称性 守恒量 |
Effects of Equivalent Transformations of Lagrange Functions on Symmetries and Conserved Quantities of Mechanics Systems |
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| DING Guang-tao.Effects of Equivalent Transformations of Lagrange Functions on Symmetries and Conserved Quantities of Mechanics Systems[J].Journal of Anhui Normal University(Natural Science Edition),2009,32(1). |
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| Authors: | DING Guang-tao |
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| Institution: | DING Guang-tao(College of Physics , Electrical Information,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | The effects of two kinds of equivalent transformations of Lagrange functions on symmetries and conserved quantities of mechanics systems are studied.Under the guage equivalent transformations,the Noether conserved quantities of systems will remain,but the Noether equality may vary and the conditions under which the Noether symmetries can be kept are given.Under the isotopic equivalent transformations,the Noether conserved quantities will still remain,but the Noether symmetries will vary and the ways to cons... |
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| Keywords: | guage equivalent transformation of Lagrange function isotopic equivalent transformation of Lagrange function Noether symmetry Lie symmetry conserved quantity |
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