共查询到18条相似文献,搜索用时 265 毫秒
1.
研究广义经典力学系统的对称性和一类新型守恒量——Mei守恒量.在高维增广相空间中建立 了系统的运动微分方程;给出了系统的Mei对称性、Noether对称性和Lie对称性的判据;得 到了分别由三种对称性导致Mei守恒量的条件和Mei守恒量的形式.举例说明结果的应用.
关键词:
广义经典力学
Mei对称性
Noether对称性
Lie对称性
守恒量 相似文献
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研究Birkhoff系统规范变换对其Noether对称性、Lie对称性和Mei对称性的影响.在一定条件下,Noether对称性和守恒量不改变.Lie对称性和Hojaman守恒量仍保持不变.Mei对称性和新型守恒量可能变化,得到了Mei对称性和新型守恒量保持不变的条件.举例说明结果的应用.
关键词:
Birkhoff系统
规范变换
对称性
守恒量 相似文献
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研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程;给出了系统的Lie对称性和Mei对称性的定义和判据;对于单面非Chetaev型非完整系统,证明了在一定条件下,由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量,由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量;研究了对称性和新守恒量之间的相互关系.文末,举例说明结果的应用.
关键词:
分析力学
单面约束
非完整系统
对称性
Hojman守恒量
Mei守恒量 相似文献
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研究广义Hamilton系统的Mei对称性导致的守恒量. 首先,在群的一般无限小变换下给出广义Hamilton系统的Mei对称性的定义、判据和确定方程;其次,研究系统的Mei守恒量存在的条件和形式,得到Mei对称性直接导致的Mei守恒量; 而后,进一步给出带附加项的广义Hamilton系统Mei守恒量的存在定理; 最后,研究一类新的三维广义Hamilton系统,并研究三体问题中3个涡旋的平面运动.
关键词:
广义Hamilton系统
Mei对称性
Mei守恒量
三体问题 相似文献
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研究事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性和Mei守恒量.建立系统的运动微分方程,给出系统Mei对称性、弱Mei对称性、强Mei对称性的定义和判据,得到由Mei对称性直接导致的Mei守恒量的存在条件以及Mei守恒量的表达式.举例说明结果的应用.
关键词:
事件空间
Nielsen方程
单面非Chetaev型非完整系统
Mei守恒量 相似文献
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In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results. 相似文献
12.
In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results. 相似文献
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研究事件空间中Birkhoff系统的Noether对称性与Noether守恒量.首先,建立了事件空间中Birkhoff系统的参数方程;其次,基于Pfaff作用量在无限小变换下的不变性,给出了事件空间中Birkhoff系统的Noether定理及其逆定理;最后,举例说明结果的应用.
关键词:
事件空间
Birkhoff系统
Pfaff作用量
Noether对称性 相似文献
15.
Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space
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Hojman conserved quantities deduced from the special Lie symmetry,
the Noether symmetry and the form invariance for a nonholonomic
system of the unilateral non-Chetaev type in the event space are
investigated. The differential equations of motion of the system
above are established. The criteria of the Lie symmetry, the Noether
symmetry and the form invariance are given and the relations between
them are obtained. The Hojman conserved quantities are gained by
which the Hojman theorem is extended and applied to the nonholonomic
system of the unilateral non-Chetaev type in the event space. An
example is given to illustrate the application of the results. 相似文献
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在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程;给出了系统的Norther对称性,Lie对称性和Mei对称性的判据;研究了三种对称性之间的关系;得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量,研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用.
关键词:
分析力学
单面约束
对称性
守恒量
相空间 相似文献
18.
In this paper, we present the fractional Hamilton's canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton's canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. 相似文献