导出的非线性微分方程存在解析积分，从而得出转体运动的一般规律，计算结果与数值积分结果相一致。
The general characteristics of the turning motion are obtained, and the results of the analytic calculation agree with those of numerical integration.
绝大多数非线性微分方程是不能用解析方法求解的。
The overwhelming majority of nonlinear differential equations are not soluble analytically.
数量和空间在解析几何，微分几何和代数几何中都发挥作用。
Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry.
由于非饱和流动的数学模型归结为非线性的偏微分方程，除了一些很特殊的情况外，很难得到解析解。
It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation.
对用加强环加强的受压长圆筒或管道(简称加强圆筒)应用薄壳力矩理论微分方程的解析解求解加强圆筒中的各项应力。
By using the analysis solution of differential equations based on thin shell theory, the stresses in pressurized long cylinder or piping stiffened with stiffeners were analyzed.
通过对CRCP微分单元的分析，推导了考虑钢筋与混凝土间及混凝土与地基间非线性粘结-滑移关系的温度应力通用解析解。
Based on the analysis of CRCP differential cell, a general analytic solution considering nonlinear bond-slip relation between steel bar and concrete and that between concrete and base is deducted.
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.
课程内容包括常微分方程、空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as ordinary differential equation vectors and analytic geometry derivatives integration and series.
本文通过建立轨道振动微分方程，得到单轮作用下轨道变形的解析表达式。
The analytical formula of track deformation under a single wheel load has been deduced by establishing the track vibration differential equation.
本章同样使用优级数法讨论一类带时滞的迭代微分方程解析解的存在性。
In this chapter, existence of analytic solutions of an iterative differential equation with state-dependent delays is studied by using a similar method.
提出了溶洞和井筒连接的试井偏微分方程数学模型，并采用正交变换法得到了其解析解。
In this paper, we found Large-scale cave and shaft connected Test partial differential equation model, and obtain its analytical solution by orthogonal transformation metho.
提出求解常微分方程的一种新的数值方法——解析离散法。
A new numerical method, analytical discrete method, for solving ordinary differential equations is proposed.
通过分析系统不动点的稳定性，得到分数阶微分系统存在混沌的解析条件。
The analytical conditions that the fractional-order differential systems remain chaotic are obtained by analyzing the stability of the fixed points of the systems.
在理想气体假设下给出了扰动流运动微分方程组的解析解；
On the assumption that the media is an ideal fluid, the analytic solution for differential equations of disturbing flow is obtained.
描述人造卫星运动的微分方程非常复杂，不可能给出解的解析表达式。
The differential equations that describe the artificial satellite motion are very complicated, and it is impossible to get the analytic express of solution.
课程内容包括空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as vectors and analytic geometry derivatives integration and series.
本文列出了一维点阵非谐振动的非线性微分方程组，并求出了这组方程在相应边值条件下的解析解。
The exact solutions of a set of non-linear differential equations with limiting conditions describing the anharmonic vibration of a one-dimensional lattice have been obtained.
这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。
The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.
通过分析GM（1 ，1 ）模型白化形式微分方程的解析表达式，导出了求解GM（ 1 ，1 ）的精确离散化模型。
By analyzing the differential equation for GM(1,1), this paper deduces one accurate discretization model to solve GM(1,1) model.
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equations.
通过建立轨道振动微分方程，得到了单轮作用下轨道变形的解析表达式。
Analytical formula of track deformation under a single wheel load was derived by establishing the differential equation of track vibration.
钟万勰院士提出的偏微分方程的子域精细积分方法是一种半解析方法，方法简单，精度高。
The Precise Integration Method in the time domain developed by Zhong is very useful to solve a kinds of differential equations because it possesses very high efficiency and accuracy.
从光线微分方程求得纤维中光线轨迹的解析解，并给出纤维透镜的高斯参数及物像计算公式。
The analytical solutions for ray paths in the fiber are obtained from the ray differential equation and the Gaussian parameters and the imaging formulas of the lens are also given.
当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。
The nonlinear equation of heat conduction is transformed into a Laplace's equation by applying the Kirchhoff transformation, and an analytic approximate solution of the equation is derived.
以分割区域d为基础将解析函数与共轭解析函数的微分中值定理推广到高阶形式。
Basing on a partition of region d, we generalize the differential mean-value theorems for analytic functions and conjugate analytic functions to a high order case.
利用待定函数法研究了非线性轨道微分方程的解析解，求出了一类情形下的四类解析解。
In this paper , the undermined function method has been used to study the analytic solution of nonlinear orbit differential equation. In a case four kinds analytic solution are given.
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equation…
对一类带耗散项非线性波动方程进行了研究，用“参数微分法”，得到其解析近似解。
This paper Studies nonlinear wave equation with dissipation items, reaching an approximate solution in the method of parameter differentiation.
列出二阶偏微分方程，采用一维方法求解得到了磁场、涡流的解析表达式。
Second order partial differential equations were given. They were solved by one-dimension method and analytical solutions for magnetic field and eddy current were obtained.
列出二阶偏微分方程，采用一维方法求解得到了磁场、涡流的解析表达式。
Second order partial differential equations were given. They were solved by one-dimension method and analytical solutions for magnetic field and eddy current were obtained.
应用推荐