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研究利用Lie对称的生成元τ(t,q,q·)和ξs(t,q,q·)来构造广义H ojman守恒 量,并讨论三种特殊情况,研究表明:Hojman守恒量是该广义守恒量的特例,且在Lie对称 的生成元的形式为τ(t,q)和ξs(t,q)时,该广义Hojman守恒量可以导出Lu tzky守恒 量,此外,还给出一个排除平凡守恒量的条件.最后,给出两个简单例子,作为所获得结果 的说明.
关键词:
动力学系统
广义Hojman定理
Lie对称
守恒量 相似文献
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This paper shows that first integrals of discrete equation of motion for
Birkhoff systems can be determined explicitly by investigating the invariance properties of
the discrete Pfaffian. The result obtained is a discrete
analogue of theorem of Noether in the
calculus of variations. An example is given to illustrate
the application of the results. 相似文献
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In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations. 相似文献
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Lie symmetries and conserved quantities of Birkhoff systems with unilateral constraints 总被引:8,自引:0,他引:8 下载免费PDF全文
In this paper we study the Lie symmetries of Birkhoff systems with unilateral constraints.We give the conditions for,and the form of,conserved quantities due to the Lie symmetries of the systems.and we also study the inverse problem of the Lie symmetries of the systems.Finally,an example is given to illustrate the application of the results. 相似文献
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The conservation laws (of first integrals) of mechanical systems are always of mathematical importance, and they are regarded as a manifestation of some profound physical principle. The modern means of finding conservation laws are mainly Noether symmetry and Lie symmetry. The Noether symmetry is an invariance of Hamiltonian action under the infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the infinites… 相似文献
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应用变换群Gr的无限小群变换的准对称性,给出了受单面约束的Brikhoff系统的Noether理论,并举例说明结果的应用.
关键词:
分析力学
单面约束Birkhoff系统
守恒量
对称性
Noether定理 相似文献
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