查询词典 calculus of variation

Chapter 7 considers application of variation methods to systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations.

第7章认为，变异的系统方法的应用与自由无限度，和第8章在变分法直接的方法处理。

In modern physics research, the calculus of variations has a broad application of law. As a solid mechanics, structural mechanics and computational mechanics of the theoretical foundation, it has important value in theory and practice on the mechanics; Variation method ruled out the perturbation of the restrictions can be widely used in many state-level and the state function in the calculation in the optical; Calculus of variations can be calculated with the parameters, we can guarantee the reliability of the results, can effectively reduce the workload of calculation, It can be said that the applications of calculus of variations are very broad.

在现代的物理学研究中，变分法有着广泛的应用：在力学上，变分法作为固体力学、结构力学及计算力学的理论基础，在理论上和实践上都有重要的价值；在光学上，变分法排除了微扰法的限制，可以广泛应用于诸多定态能级和态函数的计算中；在量子力学的应用中，具有可算出系统的参数，既可以保证计算结果的可靠性，又能有效地减少计算的工作量等的优点，可以说变分法的应用领域十分广阔。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

At the time of dealing with the fourth problem, we try calculus of variation of spending, move route transform into a line issue of the victory, Utilize Euler formula , ask and publish time running orbit after a little while most , confirm right route most, It's a pity that we can't get a satisfactory answer in a short time.

得到如下结果：在水流速度不变的情况下，年第一名的游速为，与方向与X轴成，如竞渡者以行进，则与X轴成，用时分秒，竞渡者若与对岸垂直游不可能达到终点；在不同区段内水流速度不变的情况下，竞渡者以折线前进，用时约为；在同一区段内水流速度变化情况下，竞渡者以曲线前进，用时约为。

On this basis, anoptimization algorithm library named OPTLIB is formed. The study of dynamic optimization theory is followed. To solve the problem of thecoupling of the static and the dynamic parameters of the flying vehicle design, some auxiliaryvariables are introduced to deal with them together. Then the calculus of variation is adoptedand augment form of Pontryagin's Maximum Principle is derived.

研究了飞行器设计中的典型动态优化问题——轨迹优化问题及算法，针对飞行器设计中的静态参数和动态参数互相耦合的问题，引入辅助变量将静态参数和动态参数统一处理，在此基础上用变分法推导了极大值原理的增广形式，证明了单独的静态或动态最优并不等于总体最优。

By investigating Euler\'s application of variational mathematics to mechanics, especially his principle of least action,the mechanics background of his research and its influence on Lagrange are revealed.6.By the discussion of Lagrange\'s innovation and generalization of the calculus of variations,the reason why Lagrange puts forward his method of variation by comparing Euler\'s method is explained.

深入细致地分析了拉格朗日对变(来源：ABC论文2d网www.abclunwen.com)分法所做的变革和发展：(1)通过比较欧拉方法和拉格朗日方法，探讨了拉格朗日变分方法——δ-方法提出的动因；(2)详细论述了拉格朗日早期对变分法发展所作的重要贡献；(3)探究了拉格朗日δ-方法由非参数形式向参数形式转变的原因。7。

This subject combines the basic principle of the calculus of variation and and reply and change basic theories of the function according to fracture mechanics, use mechanics, mathematics knowledge to set up corresponding mathematical model, derive out a series of mechanics and mathematics theory formula, work out procedure carry on number value calculate, to include edge crackle round stress intensity factor of component go on, ask, solve.

本课题结合变分法的基本原理并根据断裂力学和复变函数的基本理论，运用力学、数学知识建立相应的数学模型，推导出一系列的力学及数学理论公式，编制程序进行数值计算，对含边缘裂纹圆形构件的应力强度因子进行求解。

The part of calculus that deals with the variation of a function with respect to changes in the independent variable by means of the concepts of derivative and differential.

微积分学中有关用导数与微分的观念讨论函数随独立变量改变的部分。

The method of constructing arithmetic of oil system steady model for aero engine has been elaborated in this paper, which is based on the analyses of different parts characteristics that show monotone variation relationship and which introduces the notion "balanced calculation" to replace traditional iteration with vector calculus and various interpolation algorithms.

在分析滑油系统部附件的基础上，根据部附件特性单调变化的特点，提出了"平衡计算"的概念，应用向量运算方法和多种插值算法取代传统的迭代算法来构造航空发动机滑油系统稳态模型算法的思路和方法，并用该算法编制程序对发动机在海平面最大状态下滑油系统性能参数进行了验算。

It is different from the finite element method which uses the calculus of variation to construct the element-based approximate equilibrium equation. It does consider the equilibriums of forces on the inter-element boundary, which are neglected in the finite element method through the weak formulation.

这种方法跟有限元素法不同，因为有限元素法是采用变分法建立各个元素的近似平衡方程式，这种方法也考虑元素与元素相连接的边界上的力平衡条件，而在有限元素法的推导过程中我们忽略了这种条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。