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In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results. 相似文献
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The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry. 相似文献
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研究相对论性转动变质量非完整可控力学系统的非Noether守恒量——Hojman守恒量. 建立了系统的运动微分方程, 给出了系统在特殊无限小变换下的Mei对称性(形式不变性) 和Lie对称性的定义和判据, 以及系统的Mei对称性是Lie对称性的充分必要条件. 得到了系统Mei对称性导致非Noether守恒量的条件和具体形式. 举例说明结果的应用.
关键词:
相对论性转动
可控力学系统
变质量
非Noether守恒量 相似文献
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本文通过计算得到了以任意速度运动的电荷在周围空间产生的位移电流密度矢量的表达式,并且讨论了v≤c和v~c两种情况下位移电流密度矢量的分布. 相似文献
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Thestudyofconservationlawsofdynamicalsystemisasignificantaspectofmodernanalyticalmechanics.In1918,usingtheinvarianceofHamiltonactionundertheinfinitesimaltransformations,Noether[1]studiedconservationlawsofmechanicalsystemandpresentedthefamousNoether’stheor… 相似文献
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The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system 下载免费PDF全文
We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system.By means of the Lagrange-Maxwell equation,the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained.The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity.Using the Noether theorem,we obtain an approximate conserved quantity.An example is provided to prove the existence of the approximate conserved quantity. 相似文献