得到了欧氏空间中，单位球面上坐标函数关于某一特定标架场的协变微分的两个等式。
We obtain two formulas about the covariant derivative of the coordinate functions on the unit sphere in Eucdidean space.
通过非线性系统的线性化方法，讨论了一类非线性时变微分系统的解关于部分变量指数稳定的一次近似。
The first order approximation of the partial exponential stability of nonlinear time-varying systems is investigated by linearization approach of nonlinear systems.
这种控制器的设计结合了微分几何理论及变结构控制理论。
Design of these controllers combines the differential geometry theory with the variable structure control theory.
获得了一类带有连续和分段常数变元的中立型微分方程所有解振动的新的充分条件。
The new sufficient conditions for the oscillation of all solutions of the neutral differential equation with continuous and piecewise constant arguments are obtained.
在研究传统解微分方程距离保护采用固定窗长的基础上，提出了一种基于噪声水平控制的变窗长算法。
This paper presents a novel algorithm for solving differential equation of distance protection which adopts an adaptive window length based on noise level control.
本文应用哈密顿变分原理较简捷地建立了厚梁横向振动的微分方程。
The differential equation for transverse vibration in thick beam is easily established by applying the Hamilton's variance principle.
本文首次提出精确解析法，用以求解任意变系数微分方程在任意边界条件下的解。
In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary, boundary condition.
主要介绍了变结构控制、反馈线性化的微分几何方法、逆系统方法、直接反馈线性化等方法的基本思想和基本问题。
The idea and basic problem in variable structure control, differential geometry method on feedback linearization , inverse system method, direct feedback linearization method are mainly described.
对于二阶变系数线性微分方程来说，这也是可积的一个充分条件。
It is also a sufficient condition for second order linear differential equation with varied coefficient to be integrable.
为此，本文作者推导出了能精确描述变截面情况的分布参数张力微分方程。
The tension differential equation with distributed parameters which can accurately describe the tension at varied section was inferred.
本文研究了一类一阶变系数非线性滞后型微分方程解的振动性，得到这类方程仅有振动解的充分条件。
The study is made on the oscillation of a class of the first order nonlinear retarded differential equations with variable coefficients, and the sufficient conditions are obtained.
建立了具泛函变元的拟线性偏微分系统解振动的充分条件。
Sufficient conditions are established for the oscillation of systems of second order partial differential equations with functional arguments.
对二阶变系数非线性微分方程的常系数化给出两个使其可积的条件，并举例论证。
The two conditions of the second order nonlinear differential equation with variable coefficient are given and expounded with examples.
结果表明，该方法对于求解各类变系数常微分方程是十分有效的。
The result shows that it is effective for solving ordinary differential equation with variable coefficients.
本文建立了一类带偏差变元的偏微分方程边值问题解的振动准则。
In this paper some oscillation criteria are established for solutions of boundary value problems of a class of partial differential equations with deviating arguments.
它可以求解在任意边界条件下任意变系数正定或非正定偏微分方程。
It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition.
本文研究了二阶变系数线性常微分方程的一种近似求解方法。
In this paper, we study an approximate solution of the second-order linear ordinary differential equations with variable coefficients.
文章将建立了具有分段常数滞后变元微分方程组振动的一个充分条件，并讨论其非振动解的渐近性。
The present paper is devoted to the oscillations and nonoscillations of a kind of impulsive delay differential equations with piecewise constant argument.
建立了功能梯度材料中SH波的变系数微分方程。
The differential equation with varied coefficient of the SH-wave in the functionally graded materials is established.
通过构造差分方程的周期数列解，研究了一类具有分段常数变元的脉冲微分方程周期解的存在性。
The existence of periodic solutions for a class of impulsive differential equations with piecewise constant argument is studied by constructing periodic sequence solutions of difference equation.
利用变分原理得到平衡微分方程组和相应的边界条件。
By variational principle we obtain a system of differential equations and corresponding boundary conditions.
目的研究一类具有连续偏差变元的双曲偏泛函微分方程边值问题解的振动性。
Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments.
本文假设了接近砖烟囱实际截面面积的函数，推出了一个变系数的自由振动微分方程。
In this paper, a cross-section function of brick chimney has been assumed based on traditional hypothesis and a variable coefficient free-vibrating differential equation has been derived.
利用正交多项式序列的正交性及微分算子矩阵，论述了时变非线性分布参数系统参数估计的正交多项式法。
New method of parameter estimation for time varying non linear distributed systems is proposed in term of orthogonality of orthogonal polynomial and differential operation matrix.
用变分有限元方法对描述地下流体渗流的偏微分方程进行了分析。
The partial differential equation of flow in porous medium has been studied with variational finite element method.
在建立单元的能量方程后，对方程进行变分得到墙元的常微分方程。
When energy equation for element was built, variational method was used to get ordinary differential equation.
本文将研究时变退化时滞微分系统。
The time varying singular delay differential systems will be discussed.
给出系统的时间积分等式，并由此等式导出类能量方程、类维里定理、一个积分变分原理和一个微分变分原理。
A power-like equation, a Virial-like theorem, an integral variational principle and a differential variational principle for the system are deduced by using the time-integral identity.
在一个采样时间不固定，且采样信号带有噪声的应用实例中，采用变步长的跟踪微分器加预报的方法得到了较好的结果。
In a practical example, a good result is obtained by the adoption of step-varying TD and predicting under the condition of sampled signal with noise and sampled time varying.
给出了变系数二阶齐次线性常微分方程的一种积分形式解和几类变系数二阶齐线性常微分方程的普遍解。
The solutions of interal form and the general solutions of some second order homogeneous linear differential equations with variable coefficient are given.
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