共查询到18条相似文献,搜索用时 156 毫秒
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研究奇异系统Hamilton正则方程的形式不变性即Mei对称性,给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系,寻求系统的守恒量.给出一个例子说明结果的应用.
关键词:
奇异系统
Hamilton正则方程
约束
对称性
守恒量 相似文献
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研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据,得到形式不变性的结构方程和守恒量的形式,并举例说明结果的应用.
关键词:
相空间
二阶线性非完整系统
形式不变性
守恒量 相似文献
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研究非完整力学系统的形式不变性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下,给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程,提出并定义弱(强)形式不变性的概念. 研究特殊形式不变性导致特殊Lie对称性的条件,由系统的特殊形式不变性,得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出两个经典例子说明结果的应用.
关键词:
分析力学
非完整系统
形式不变性
非Noether守恒量
Hojman守恒量 相似文献
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在时间不变的特殊无限小变换下,研究相对论性变质量非完整可控力学系统的非Noether守恒量——Hojamn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形式不变性(Mei对称性)的定义和判据以及系统的形式不变性是Lie对称性的充分必要条件.得到了系统形式不变性导致非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
非完整可控力学系统
变质量
非Noether守恒量 相似文献
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基于函数对时间的全导数采用沿系统的运动轨线方式, 研究非Chetaev型非完整可控力学系统的Noether-形式不变性. 给出非Chetaev型非完整可控力学系统的Noether-形式不变性的定义和判据. 由Noether-形式不变性同时得到了Noether守恒量和新型守恒量. 并举例说明结果的应用.
关键词:
非Chetaev型非完整系统
可控力学系统
Noether-形式不变性
守恒量 相似文献
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Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system 下载免费PDF全文
A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results. 相似文献
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A form invariance of Raitzin's canonical equations of
relativistic mechanical system is studied. First, the Raitzin's canonical
equations of the system are established. Next, the definition and criterion
of the form invariance in the system under infinitesimal transformations of
groups are given. Finally, the relation between the form invariance and the
conserved quantity of the system is obtained and an example is given to
illustrate the application of the result. 相似文献
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A form invariance and a conserved quantity of the generalised Birkhoffian system are studied.
Firstly, a definition and a criterion of the form invariance are given. Secondly, through the form invariance,
a new conserved quantity can be deduced. Finally,
an example is given to illustrate the application of the result. 相似文献
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Using form invariance under special infinitesimal transformations
in which time is not variable, the non-Noether conserved quantity
of the relativistic nonholonomic system with variable mass is studied.
The differential equations of motion of the system are established.
The definition and criterion of the form invariance of
the system under infinitesimal transformations are studied.
The necessary and sufficient condition under which the form
invariance is a Lie symmetry is given. The condition under
which the form invariance can be led to a non-Noether conserved
quantity and the form of the conserved quantity are obtained.
Finally, an example is given to illustrate the application of the result. 相似文献
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Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass 总被引:1,自引:0,他引:1 下载免费PDF全文
Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result. 相似文献
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This paper focuses on studying non-Noether conserved quantities of Lie
symmetry and of form invariance for a mechanical system in phase space
under the general infinitesimal transformation of groups. We obtain a new
non-Noether conserved quantity of Lie symmetry of the system, and Hojman and
Mei's results are of special cases of our conclusion. We find a
condition under which the form invariance of the system will lead to a Lie
symmetry, and, further, obtain a new non-Noether conserved quantity of form
invariance of the system. An example is given finally to illustrate these
results. 相似文献