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A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results. 相似文献
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研究相对论性变质量系统的守恒律.给出相对论性变质量系统的d’Alembert-Lagrange原理,利用其在无限小变换下的不变性条件,得到相对论性变质量系统的守恒律存在的条件和形式,并举例说明结果的应用
关键词:
相对论
分析力学
变质量
守恒律 相似文献
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研究了具有单面约束的Birkhoff系统在小扰动作用下对称性的摄动与不变量之间的关系.首先,建立了系统的运动微分方程,给出了系统的精确不变量;其次,基于力学系统的高阶绝热不变量的概念,得到了系统的绝热不变量存在的条件及其形式;最后,举例说明结果的应用
关键词:
分析力学
单面约束
Birkhoff系统
对称性
摄动
绝热不变量 相似文献
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A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics 总被引:1,自引:0,他引:1 下载免费PDF全文
The perturbations to symmetries and adiabatic invariants for nonconservative systems
of generalized classical mechanics are studied. The exact invariant in the form of
Hojman from a particular Lie symmetry for an undisturbed system of generalized
mechanics is given. Based on the concept of high-order adiabatic invariant in
generalized mechanics, the perturbation to Lie symmetry for the system under the
action of small disturbance is investigated, and a new adiabatic invariant for the
nonconservative system of generalized classical mechanics is obtained, which can be
called the Hojman adiabatic invariant. An example is also given to illustrate the
application of the results. 相似文献
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EFFECTS OF NON-CONSERVATIVE FORCES ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF A LAGRANGE SYSTEM 总被引:1,自引:0,他引:1 下载免费PDF全文
Non-conservative forces are exerted on a Lagrange system. Their effects on Lie symmetries, structure equation and conserved quantities of the system are studied. It can be seen that some Lie symmetries disappear and some new Lie symmetries emerge. Under certain conditions, some Lie symmetries will still remain present. 相似文献
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WANG Peng FANG Jian-Hui DING Ning ZHANG Xiao-Ni 《理论物理通讯》2007,48(4):615-618
In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results. 相似文献
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利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式.
关键词:
非完整系统
伺服约束
Lie对称性
守恒量 相似文献
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在p-T图上,通过饱和蒸汽作绝热膨胀的斜率与气液平衡曲线的斜率的大小比较,来判断饱和蒸汽绝热膨胀后对应的单相态。 相似文献
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EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS 总被引:1,自引:0,他引:1 下载免费PDF全文
After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain. 相似文献
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在研究精密电容器的几何尺寸误差引起的电容量误差时, 往往需在不规则边界的边值条件下求解拉普拉斯方程. 这里提供种解决这类问题的计算方法—-“变动边界微扰法”, 并给出了微扰过程的收敛条件. 在此方法的基础上, 还求出了电极系统有任意变形时电荷量变化的一般计算公式. 把这些结果应用于Lampard-Tamompson 型的计算电容时, 可以证明关于这种电容器的一些普遍性质.
关键词: 相似文献
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Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems 下载免费PDF全文
Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results. 相似文献