共查询到17条相似文献,搜索用时 78 毫秒
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互补变分原理及其在微扰理论近似中的应用 总被引:1,自引:0,他引:1
以正则变分和线性变分函数为基础,对互补变分原理作了论证,推导出二阶能量修正的上界和不受任何条件限制的下界,对具体计算方法作了详细的研究,得出互补变分原理在微扰理论近似中的应用,所求氢原子和极化率结果比一般的发法的微扰法所得结果更接近于实验值,并指出这理论可以推广应用到激发态或处理高阶修正问题。 相似文献
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给出了广义经典力学系统的变分方程,研究了变分方程的解与系统的第一积分之间的联系,并证明可由系统的第一积分求得变分方程的特解.
关键词:
广义经典力学系统
第一积分
变分方程 相似文献
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LUO En LIANG LiFu & LI WeiHua Department of Applied Mechanics Engineering Sun Yat-sen University Guangzhou China Department of Aerospace Engineering Harbin Engineering University Harbin China 《中国科学G辑(英文版)》2007,50(2):152-162
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper. 相似文献
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研究事件空间中力学系统的微分变分原理.基于D'Alembert原理,建立了事件空间中力学系统的D'Alembert-Lagrange原理、Jourdain原理、Gauss原理和万有D'Alembert原理,给出了这些原理的Euler-Lagrange参数形式、Nielsen参数形式和Appell参数形式,并导出了万有D'Alembert原理的Mangeron-Deleanu参数形式.
关键词:
分析力学
事件空间
微分变分原理 相似文献
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ZhenBang Kuang 《中国科学G辑(英文版)》2008,51(9):1390-1402
It is proposed that the universal thermodynamic energy variational principle is included in the first law of thermodynamics.
Some variational principles in the electroelastic media under finite deformation are derived from this universal thermodynamic
variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together
with the discussed electroelastic medium. For the variational principle of nonlinear electroelastic media the variation of
the electric potential is coupled with the virtual displacement, and the variation of the initial volume should be considered.
The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the
second order precision.
Supported by the National Natural Science Foundation of China (Grant No. 10472069) 相似文献
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Eugene P. Gross 《Journal of statistical physics》1973,9(4):297-315
Aspects of stationary variational principles for the Laplace-transformed Liouville equation are discussed. Projection techniques are used to derive new stationary principles applicable to the space orthogonal to the space spanned by functions occurring in the conservation laws. As a result, any trial function automatically leads to results satisfying the conservation laws. The procedure is also applied to the parity-even and parity-odd distributions which obey equations governed by the square of the Liouville operator. The technique is extended to eliminate the one-body additive contribution to the solution exactly. Finally, the ideas of the moment method, which leads to the continued-fraction representation of autocorrelation functions, are applied to variational principles. We find continued-fraction variational principles such that a zero trial function yields the usual representation. However, a trial function representing noninteracting particles contains the results of the moment method and in addition yields the exact analytic behavior for free particles.Work supported by a grant from the National Science Foundation. 相似文献