1) principle of total potential energy with stationary value
总势能不变值原理
1.
This paper discusses the inadequacies in Lagrange s equations and in Hamilton s principle and introduces the principle of total potential energy with stationary value in elastic system dynamics and the "Set in right position" rule for formulating matrixes, both were first presented by Zeng Qing yuan 22 years ago.
讨论了拉格朗日方程和哈密顿原理的不足 ,介绍了由曾庆元 2 2年前首次提出的弹性系统动力总势能不变值原理及形成系统矩阵的“对号入座”法则 ,阐明了不论系统如何复杂 ,其空间振动方程均可利用此原理和此法则简便建立 。
2) principle of invariable potential energy
势能不变值原理
1.
Concludes and analyses the physical notion and mathematical method of the principle of resident potential energy, furthermore deducing the derivative principles: principle of invariable potential energy, principle of least potential energy and Timoshenko energy method, the applicable conditions of which are narrated, making the physical and mathematical notions consistent.
对能量法中势能驻值原理的物理概念和数学方法进行整理、归纳和明析,进而推演出该原理的派生原理:势能不变值原理、最小势能原理和Timoshenko能量法,使各基本原理的物理和数学概念协调统一。
3) principle of total potential energy with stationary value
动力学总势能不变值原理
1.
The principle of total potential energy with stationary value in system of particles and its application;
动力学总势能不变值原理在质点系建模中的应用
2.
The differential equation is deduced by using the principle of total potential energy with stationary value.
文章对滚动轴承故障试验台进行了理论建模分析,建立了试验台的动力学模型,并应用质 点系动力学总势能不变值原理推导出试验台的运动微分方程。
4) principle of resident potential energy
势能驻值原理
1.
Concludes and analyses the physical notion and mathematical method of the principle of resident potential energy, furthermore deducing the derivative principles: principle of invariable potential energy, principle of least potential energy and Timoshenko energy method, the applicable conditions of which are narrated, making the physical and mathematical notions consistent.
对能量法中势能驻值原理的物理概念和数学方法进行整理、归纳和明析,进而推演出该原理的派生原理:势能不变值原理、最小势能原理和Timoshenko能量法,使各基本原理的物理和数学概念协调统一。
2.
By collecting,generalizing and analyzing the physical concept and mathematical method of the principle of resident potential energy,it deduces the derivative principles: principle of resident and invariable potential energy and Timoshenko energy method.
对势能驻值原理的物理概念和数学方法进行整理、归纳和明析,进而推演出该原理的派生原理:势能不变值原理、最小势能原理和Timoshenko能量法,对各原理的适用条件进行了阐述,使各基本原理的物理和数学概念形成协调统一。
3.
Based on the principle of resident potential energy,a nonlinear differential equation of static beams with the nonlinear effect of dead loads is included,and the effect of the dead loads on deflection of cantilever beams is studied by Galerkin method.
应用势能驻值原理,推导出恒载对梁活载挠度影响的非线性微分方程,通过Galerkin方法研究了恒载对悬臂梁活载挠度的影响。
5) principle of stationary potential energy
势能驻值原理
1.
The equation of relationship between the top displacement and the rod angle of frame structure is established according to the principle of stationary potential energy.
根据势能驻值原理建立了框架顶部侧移和杆端转角之间的关系方程,推导出框架结构在水平节点荷载作用下的顶部侧移计算公式,方法简便适用,且计算精度较高,为框架结构顶部侧移的计算提供了一种新的简便计算方法,得出了用D值法求得的框架顶部侧移一般比实际侧移偏大的结论。
2.
Differential equations are obtained according to the principle of stationary potential energy.
根据势能驻值原理,推导得到了平衡微分方程。
6) Principle of potential energy
势能驻值原理
补充资料：变分原理(复变函数论中的)
变分原理(复变函数论中的)
omplex function theory) variational principles (in
f日In}F(O(只，t)，0)l}乙+:d乙=】nll，—}——，厂:’、一几t)〔.匕，日亡卜OC一“C’日当r，0时下*(:、，t)/:在B*的紧子集上一致地趋于0(k一1，2).该结果已被推广到二连通区域(13」).若加以进一步的限制，就能得到映射函数在B、(t)内关于表征所考虑区域边界形变的参数的展开式余项的估计式(在闭区域内一致)(【4」).份卜注】存在大量的变分原理，见【A3}第10章.亦可见变分参数法(variation一parametrie nlethod);肠”ner方法(幼wner Tnetl〕ed);内变分方法(internalvariations，服t】1‘对of). 还可见边界变分方法(boundary variations，me-tll‘xlof).M.schiffer对单叶函数的变分方法做出了重要的贡献，见〔A3」第10章.变分原理(复变函数论中的)Ivaria石0“目州址妙es(加e网Plex五叮‘6佣山印ry);。即“a双“OHH从e nP一”u“nHI 显示在平面区域的某些形变过程中那些支配映射函数变分的法则的断语. 主要的定性变分原理是ljxlelbf原理(Linde场fpnnciPle)，可描述如下.设B*是z*平面上边界点多于一点的单连通区域，06B*，k=1，2;设二(;，B*)是对于B*的Green函数的阶层曲线，即圆盘王心川C!<1}到B*而使原点保持不变的单叶共形映上映射下圆周C(r)二{乙:{心}二;}的象，o<;<1.进而设函数f(:，)实现B，到B:的共形单射，f(0)‘O，在这些假定下有:l)对于L(:，B，)上任一点:?，存在位于阶层曲线L(:，BZ)上(这仅当f(B，)二BZ才有可能)或其内部的一点与之对应;及2){f’(0)1蕊}夕‘(0)}，其中g(:，)满足g(0)二o是Bl到 BZ的单叶共形映射(等号仅当f(B1)=B:时成立).Lindebf原理系从Rien坦nn映射定理(见Rle-n.lln定理(Rierl飞幻In theorem))与Sdlwarz引理(Schwarz lemrr必)推出.相当精细的构造使之能够求出由被映射区域的给定形变所引起的映射函数的逐点偏差. 定量的基本变分原理系由M.A.几aBpeHTbeB(〔1」)获得(亦可见【2])，可叙述如下，设B:是具有解析边界的单连通区域，0任B!.假定存在给定区域族B，(r)，0‘Bl(r)，0(t蕊T，T>O，B;(0)二B，，具有JOrdan边界rl(t)={:一z，=0(之，t)}，0(又续2兀，0(0，t)二Q(2二，r)，其中Q(又，r)关于t在t二O可微且对又是一致的;设F(::，t)，F(0，t)=0，F:.(0，t)>O，是把B，(t)单叶共形映射为BZ二{22:I:21
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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