我们马上就要学习直线的参数方程。
OK, so we are going to learn about parametric equations of lines.
那是球体的一个参数方程。
实际上，直线的参数方程总是这个样子的。
In fact, parametric equations of lines always look like that.
我不准备写参数方程。
有曲面的参数方程。
并采用单参数方程对实验数据进行了关联。
The experimental data are correlated with a simple parameter equation.
我希望在这明白,参数方程是考虑直线的一个很好办法。
So, I hope you've seen here that parametric equations are a great way to think about lines.
而当我们考虑运动点的轨迹的时候，轨迹可以称作是参数方程。
And, so when we think of the trajectory of the moving point, that's called a parametric equation.
再来深入研究一下参数方程，我们以前还学过速度和加速度的。
Ok, so let me move on a bit and point out that with parametric equations, we've looked also at things like velocity and acceleration.
提出了任意转角位置的渐开线齿轮齿廓的参数方程。
The parameter equation of involute tooth profile on any angular position is presented.
本文给出了抛物环面天线的参数方程和辐射场公式。
In this paper, the parametric equation and radiation field formulas for a parabolic torus reflector antenna are given.
椭圆的参数方程的几何意义是众所周知的(见例1)。
The geometric meaning for the parametric equation of ellipse is a familiar thing (See example 1).
文中的曲面或用参数方程表达或用符号距离函数表达。
In this paper, the surface is presented with a parameterized equation or a signed distance function.
在初参数方程的求解中，利用了初参数影响系数矩阵。
The influence coefficient matrixes of initial parameter are used for the solutions of the initial parameter equations.
讨论了迁移理论中一类控制临界参数方程的求解问题。
In this paper, a class of the control critical parametric equations, which arises in transport theory is discussed.
首先说明了参数方程的基本定义，了解什么是参数方程。
Firstly illustrates the basic definition parameter equation, understand what is the parameter equation.
各向异性的伤演规律可由能量平衡及当量单参数方程所确定。
The anisotropic damage evolution law is obtained by the virtue of energy equilibrium and an equivalent singe variable equation.
我们主要还是关注，参数方程的运用，主要是一维的，比如直线、曲线等。
So, we have mostly focused on the use of parametric equations just for one dimensional objects, lines, and curves.
然后针对给定参数方程的曲线，提出一种圆弧拟和的实用算法。
And then, we provide an algorithm for approximating an arbitrary parametric curve by circular arcs.
现在我们可以做很多事情了，因为我们有了参数方程，现在有一件神秘的事。
So, now, just to show you that we can do a lot of things when we have a parametric equation, here is a small mystery.
凡是可以表示为矢量参数方程的正则曲线，都可以用该方法进行插补。
Any regular curve that can be expressed by the vector parameter equation may be interpolated by this method.
我们还学过怎样理解直线方程，它们有些特性，因为我们是从参数方程角度理解。
Ok, we've also seen how to look at equations of lines, and those were of a slightly different nature because we've been doing them as parametric equations.
我们建立有两个变量φ和θ的球面的参数方程,它们恰好是,球坐标系统的一部分。
We are finding a parametric equation for the sphere using two variables phi and theta which happen to be part of the spherical coordinate system.
本文将分别对双曲线、抛物线的参数方程阐述几何意义(见例2、例3)。
This paper describes the geometric meaning for the parametric equation of hyperbola and parabola, respectively (see examples 2 and 3).
运用毕奥萨伐尔定律和椭圆参数方程，计算出椭圆环电流中心的磁感强度。
The magnetic induction intensity at the center of elliptic current ring is derived based on the Biot-Savart law and elliptic parameter equation intensity.
第6周隐函数的导数。由参数方程所确定的函数的倒数。数学实验一。 二。
Week 6 The derivative of implicit function. the function's derivate by parameter equation.
本文详细推导了小型高频引弧器的参数方程，为参数分析和设计提供了理论依据。
The parameter equations of a small high-frequency are starter are obtained in this paper, and such equations provide theoretical basis for the ana - lysis and design of the parameters.
同时，对具有参数方程形式表示的非圆曲线进行了等间距直线逼近的节点误差分析。
While there is the analysis of node tolerance with parameter equation on approaching along a straight line with equal step.
求由参数方程所确定的函数的高阶导数，提出了一种较为直观、简便的逐次求导方法。
Author presented a concise gradual derivation about higher derivative whose function defined by parametric equation.
给出了多项式参数方程定义的参数曲线的有效隐式化算法，此算法主要是基于矩阵理论。
This paper presents an efficient algorithm for the implicitization of parametric curves defined by polynomial parametric equations, which is mainly based on the theory of matrices.
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