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1.
对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系统 ,基于广义Apell_Четаев约束条件 ,并考虑到系统的内在约束 ,导出了该非完整约束奇异广义力学系统的广义Poincar _Cartan积分不变量 .并证明了该不变量与非完整约束奇异广义力学系统的广义正则方程等价  相似文献   

2.
对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系统,基于广义Apell-Чqeraea约束条件,并考虑到系统的内在约束,导出了该非完整约束奇异广义力学系统的广义Poineare-Cartan积分不变量.并证明了该不变量与非完整约束奇异广义力学系统的广义正则方程等价.  相似文献   

3.
非完整约束奇异广义力学系统的Poincaré-Cartan积分   总被引:1,自引:0,他引:1       下载免费PDF全文
李爱民  张莹  李子平 《物理学报》2004,53(9):2816-2820
对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系 统,基于广义Apell-Четаев约束条件,并考虑到系统的内在约束,导出了该非完整 约 束奇异广义力学系统的广义Poincaré-Cartan积分不变量. 并证明了该不变量与非完整约束 奇异广义力学系统的广义正则方程等价.  相似文献   

4.
转动相对论Birkhoff约束系统积分不变量的构造   总被引:1,自引:0,他引:1       下载免费PDF全文
研究转动相对论Birkhoff约束系统积分不变量的构造首先,建立转动相对论系统的约束Birkhoff方程;其次,利用等时变分与非等时变分之间的关系建立系统的非等时变分方程;然后,研究转动相对论Birkhoff约束系统的第一积分与积分不变量之间的关系,证明由系统的一个第一积分可以构造一个积分不变量,并给出自由Birkhoff系统的相应结果;最后,讨论转动相对论Hamilton系统、相对论Birkhoff系统和Hamilton系统、经典转动系统和等时变分情形下的积分不变量的构造,结果表明相关的结论均为该定理的特款给出一个例子说明结果的应用 关键词: 转动相对论 Birkhoff系统 约束 第一积分 积分不变量  相似文献   

5.
转动相对论系统动力学的积分理论   总被引:10,自引:0,他引:10       下载免费PDF全文
罗绍凯  陈向炜 《物理学报》2001,50(11):2053-2058
建立转动相对论系统动力学方程的积分理论.给出系统运动的第一积分,分别利用系统的循环积分和能量积分降阶运动方程,得到推广的Routh方程和推广的Whittaker方程,建立系统运动的正则方程和变分方程,并由第一积分构造系统的积分不变量.给出系统的Poincaré-Cartan型积分变量关系和积分不变量. 关键词: 转动相对论 运动方程 积分方法  相似文献   

6.
准坐标下广义力学系统的Lie对称定理及其逆定理   总被引:62,自引:2,他引:60       下载免费PDF全文
研究准坐标下广义力学系统的Lie对称性与守恒量.首先,对准坐标下广义力学系统定义无限小生成元,并应用微分方程在无限小变换下不变性的Lie方法,建立系统的确定方程.其次,给出结构方程和守恒量的形式.最后,研究Lie对称性逆问题(由已知积分求Lie对称)并举例说明结果的应用. 关键词: 广义力学 准坐标 Lie对称 确定方程 结构方程 守恒量  相似文献   

7.
高维增广相空间中广义力学系统的对称性和不变量   总被引:5,自引:0,他引:5       下载免费PDF全文
依据广义增广相空间中的Hamilton作用量在无穷小变换群作用下的不变性,给出广义完整保守和非保守力学系统的对称性和不变量及有关结论的逆命题,最后举一实例说明 关键词: 增广相空间 广义力学 对称性 不变量  相似文献   

8.
非完整力学系统的Noether-Lie对称性   总被引:2,自引:0,他引:2       下载免费PDF全文
方建会  丁宁  王鹏 《物理学报》2006,55(8):3817-3820
研究了非完整力学系统的一种新对称性——Noether-Lie对称性及其守恒量. 给出了非完整力学系统Noether -Lie对称性的定义和判据,提出系统的Noether-Lie对称性导致Noether守恒量和广义Hojman守恒量的定理. 举例说明了结果的应用. Hojman守恒量是所给出的广义Hojman守恒量的特例. 关键词: 非完整力学系统 Noether-Lie对称性 Noether守恒量 广义Hojman守恒量  相似文献   

9.
研究广义线性非完整力学系统的Lie对称性导致的Hojman守恒量,在时间不变的特殊Lie对称变换下,给出系统的Lie对称性确定方程、约束限制方程和附加限制方程,得到相应完整系统的Hojman守恒量以及广义线性非完整力学系统的弱Hojman守恒量和强Hojman守恒量,并举一算例说明结果的应用.  相似文献   

10.
广义经典力学系统对称性的摄动与绝热不变量   总被引:9,自引:1,他引:8       下载免费PDF全文
张毅  梅凤翔 《物理学报》2003,52(10):2368-2372
在高维增广相空间中研究广义经典力学系统的精确不变量和绝热不变量.建立了该空间中系 统的对称性与不变量的关系;基于力学系统受到小干扰力作用的高阶绝热不变量的概念,给出了系统的高阶绝热不变量的形式及存在条件,并建立了绝热不变量与对称变换之间的对应关系;最后,举例说明结果的应用. 关键词: 对称性 摄动 不变量 广义经典力学系统 增广相空间  相似文献   

11.
We consider the 0 limit of the quantum dynamics generated by the HamiltonianH()=–(2/2m)+V. We prove that the evolution of certain Gaussian states is determined asymptotically as 0 by classical mechanics. For suitable potentialsV inn3 dimensions, our estimates are uniform in time and our results hold for scattering theory.Supported in part by the National Science Foundation under Grant PHY 78-08066  相似文献   

12.
Levesque and Verlet developed a time-reversible and bit-reversible computational leapfrog algorithm. Their algorithm uses integer arithmetic and is exactly time reversible to the last computational bit describing the particle coordinates. We generalize their idea, developed for atomistic molecular dynamics, to smoothed-particle continuum mechanics. In the special case of a two-dimensional isentropic ideal gas, these two approaches, one microscopic and the other macroscopic, are isomorphic. In the more general nonadiabatic case, but still without dissipative terms, our continuum extension of the leapfrog scheme remains stable and also exhibits the exact time and bit reversibility associated with Levesque and Verlet's atomistic approach.  相似文献   

13.
After reviewing the foundations of special relativity and the room left for rival theories, a set of nonrelativistic para-Lorentzian transformations is derived uniquely, based on (a) a weaker first principle, (b) the requirement that the transformations sought do not give rise to the clock paradox (in a refined version), and (c) the compliance of the transformations with the classical experiments of Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell. The corresponding dynamics is developed. Most of the experimental support of special relativity is reconsidered in the light of the new theory. It is concluded that the relativity of simultaneity has so far not been tested.Partially financed by Colciencias.  相似文献   

14.
Quantum theory accepts the point-like indivisible (classical) character of a particle as a mere product of a measuring process, or what has become known as a collapse. Following the notion of empty waves, which accepts the particle as a real existent entity without regard to the measurement process, we propose an experiment that may shed some light on the reality of the particle and the consequences of that reality.  相似文献   

15.
We first present a realistic framework for quantum probability theory based on the path integral formalism of quantum mechanics and illustrate this framework by constructing a model that describes a quantum particle evolving in a discrete space-time lattice. We then present a finite model for describing the internal dynamics of elementary particles and show that this model gives the standard particle classification scheme and successfully predicts particle masses.  相似文献   

16.
Statistical causality is recommended as the name of the generalized causality needed in quantum mechanics, instead of statistical correspondence used by Pauli.  相似文献   

17.
Three approaches concerning the usage of modalities in the language of quantum mechanics were considered; Mittelstaedt and I built up a dialog semantics for modalities on a metalinguistic level, and a calculus of quantum modal logic is known that is complete and sound with respect to this dialogic semantics. Van Fraassen replaced the usual interpretation of quantum mechanics (with the projection postulate) by his modal interpretation based on a modal object language. Dalla Chiara translated a nonmodal object language for quantum mechanics and the appropriate quantum logic into a modal language. Specifically we are interested in the similarities and the differences of these three approaches.  相似文献   

18.
Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional manifold of instantaneous pure states. This geometrical structure can accommodate generalizations of quantum mechanics, including the nonlinear relativistic models recently proposed. It is shown that any such generalization satisfying a few physically reasonable conditions would reduce to ordinary quantum mechanics for states that are near the vacuum. In particular the origin of complex structure is described.  相似文献   

19.
20.
The similarities between cosmology and celestial mechanics are discussed from the scientific and historical points of view and the scientific aims of these two fields are compared. Newton's and Poincaré's contributions to celestial mechanics, dynamics, and cosmology are presented. The recently established instability of triple stellar configurations is discussed to relate results of this classical, nonintegrable problem of celestial mechanics to cosmology and to offer an example for order out of chaos. It is shown that the presently emphasized reasons for limited predictability in dynamical systems are closely related to some of the existing basic difficulties in cosmology.  相似文献   

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