共查询到20条相似文献,搜索用时 187 毫秒
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针对嫦娥三号软着陆轨道设计与控制策略问题,在合理假设的前提下,建立动力学模型,求解得到了嫦娥三号着陆准备轨道近月点和远月点的速度。针对软着陆过程的6个阶段,通过受力分析,建立了嫦娥三号运动的微分方程模型,以燃料消耗最小为优化目标,以每个阶段的起止状态为约束条件,将软着陆轨道的优化设计问题转化为主发动机推力的泛函极值问题,并将其控制函数转化为近似的多项式函数优化问题。运用四阶Runge-Kutta差分迭代方法进行求解计算,从而得到各个阶段的最优控制函数和控制策略。结果表明,嫦娥三号软着陆过程耗时695s,消耗燃料1 269.1kg。 相似文献
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该文研究一类时滞方程解的展开问题. 研究的模型来自于实际高精密切割过程中具有时间延迟的机床振动问题. 对此模型,借助于泛函分析方法,将其写成抽象发展方程. 对系统确定的算子给出了较细致的谱分析,得到本征值的渐近表达式.同时证明相应的本征向量不能构成状态空间基, 但给出方程解的展开式. 相似文献
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将向量值优化问题的适定性理论推广到具有W-距离的拟度量空间中,给出B-适定性及DH-适定性的概念,并得到相应的判别准则.定义一类非线性标量化函数,利用这类标量化函数的性质将向量值优化问题转化为标量值优化问题,得到原问题与标量化问题的适定性之间的等价关系. 相似文献
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本文主要研究三峡梯级水电站与华中、华东和川东电网联网的短期经济调度问题,利用泛函分析和运筹学相结合的方法建立了三峡梯级水电站日负荷最优分配的数学模型。本文扩充和推广了Hawary和Christensen的最小范数法用来求解这个具有等式和不等式约束的高维非线性含时滞的动态最优化问题,最优策略由一组动态的非线性代数、微分方程确定。引入适当的变量并进行适当化简,最终可将三峡梯级水电系统的经济调度问题转化为一个最小范数问题,并给出了最优解的具体表达式.用Lagrange乘子和Kuhn-Tucker乘子将约束条件并入目标函数中形成一个增广价格函数。通过变换可将该无约束优化问题转化为求解非线性代数方程组的问题。本文选用Fletcher-Reeves共轭梯度法求解无约束极值问题.在IBM-PC型微机上进行了试算。试算结果表明用最小范数法求解三峡梯级水电站日负荷最优分配问题是完全可行的,梯级水耗率有明显下降,能获得一定的经济效益。 相似文献
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截断奇异值分解是一类非常重要的矩阵分解,其在病态模型问题分析等领域有广泛的应用.该文主要研究复矩阵截断奇异值分解的有效算法,将问题转化为复Stiefel乘积流形上的黎曼优化问题,进而设计基于乘积流形的黎曼混合牛顿法求解.为有效求解黎曼牛顿方程,从降低系统维数和简化计算入手,通过克罗内克积和复矩阵拉直算子将其转化为易于求解的标准实对称线性方程组.数值实验和数值比较验证该文所提算法针对复矩阵截断奇异值分解问题是高效可行的. 相似文献
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文章研究了一类结构为非线性-线性-线性三:层规划问题的求解方法.首先,基于下层问题的Karush-Kuhn-Tucker (K-K-T)最优性条件,将该类非线性三层规划问题转化为具有互补约束的非线性二层规划,同时将下层问题的互补约束作为罚项添加到上层目标;然后,再次利用下层问题的K-K-T最优性条件将非线性二层规划转化为非线性单层规划,并再次将得到的互补约束作为上层目标的罚项,构造了该类非线性三层规划问题的罚问题.通过对罚问题性质的分析,得到了该类非线性三层规划问题最优解的必要条件,并设计了罚函数算法.数值结果表明所设计的罚函数算法是可行、有效的. 相似文献
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This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to separable ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability. 相似文献
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面向客户定制模式的供应链管理系统优化模型 总被引:1,自引:0,他引:1
建立供应链管理系统优化模型是构建高效率供应链以及发挥供应链优势的前提和基础 .本文建立了面向客户定制模式的集成的供应链管理系统优化模型 ,即一个多目标、具有约束的非线性混合规划模型 ,并提出了针对这种模型的求解思路 .通过对模型的仿真求解既可以优化选择供应链系统中涉及的相关协作企业 ,同时优化系统的订货、生产、库存策略 ,对构建高效率供应链管理系统具有重要意义 . 相似文献
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A. Lesfari 《Aequationes Mathematicae》2011,82(1-2):165-200
This article is dedicated to one of the greatest mathematicians of our time: V.I. Arnold, who died suddenly Thursday, June 3, 2010 in France. Integrable hamiltonian systems are nonlinear ordinary differential equations described by a hamiltonian function and possessing sufficiently many independent constants of motion in involution. The regular compact level manifolds defined by the intersection of the constants of motion are diffeomorphic to a real torus on which the motion is quasi-periodic as a consequence of the following purely differential geometric fact: a compact and connected n-dimensional manifold on which there exist n vector fields which commute and are independent at every point is diffeomorphic to an n-dimensional real torus and each vector field will define a linear flow there. We make a careful study of the connection with the concept of completely integrable systems and we apply the methods to several problems. 相似文献
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Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its
two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy
uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov
functional for the system. 相似文献
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D. COUTAND 《数学年刊B辑(英文版)》1999,20(3):279-296
The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo has justified the two-dimensional nonlinear “membrane“ equations for a plate made of a Saint Venant-Kirchhoffmaterial, 相似文献
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D. COUTAND 《数学年刊A辑(中文版)》1999,20(3):279-296
The formal asymptotic analysis of D. Fox, A. Raoult
$\&$ J.C. Simo$^{[10]}$ has justified the two-dimensional
nonlinear ``membrane' equations for a plate made of a Saint
Venant-Kirchhoff material.
This model, which retains the material-frame indifference of the
original three dimensional problem in the sense that its energy density is
invariant under the rotations of $\R^3$, is equivalent to finding the
critical points of a functional whose nonlinear part depends on the first
fundamental form of the unknown deformed surface.
The author establishes here, by the inverse function theorem, the existence
of an injective solution to the clamped membrane problem around particular
forces corresponding physically to an ``extension' of the membrane.
Furthermore, it is proved that the solution found in this fashion is also the
unique minimizer to the nonlinear membrane functional, which is not
sequentially weakly lower semi-continuous. 相似文献
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基于曲率插值的大变形梁单元 总被引:1,自引:1,他引:0
线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析.传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题.该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数.由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题.因而所提方法特别适用于梁的几何非线性分析.数值算例说明了所提方法的正确性和有效性. 相似文献
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Hans-Christoph Grunau 《Milan Journal of Mathematics》2009,77(1):171-204
The linear clamped plate boundary value problem is a classical model in mechanics. The underlying differential equation is elliptic and of fourth order. The latter is a peculiar feature with respect to which this equation differs from numerous equations in physics and engineering which are of second order. Concerning the clamped plate boundary value problem, “linear questions” may be considered as well understood. This changes completely as soon as one poses the simplest “nonlinear question”: What can be said about positivity preserving? Does a plate bend upwards when being pushed upwards? It is known that the answer is “no” in general. However, there are many positivity issues as e.g. “almost positivity” to be discussed. Boundary value problems for the “Willmore equation” are nonlinear counterparts for the linear clamped plate equation. The corresponding energy functional involves curvature integrals over the unknown surface. The Willmore equation is of interest in mechanics, membrane physics and, in particular, in differential geometry. Quite far reaching results were achieved concerning closed surfaces. As for boundary value problems, by far less is known. These will be discussed in symmetric situations. This survey article reports upon joint works with A. Dall’Acqua, K. Deckelnick (Magdeburg), S. Fröhlich (Free University of Berlin), F. Gazzola (Milan), F. Robert (Nice), Friedhelm Schieweck (Magdeburg) and G. Sweers (Cologne). 相似文献