That is our convention to get a unit normal vector that points to the right of the curve as we move along the curve.
这是约定的得到单位法向量的方法，这种做法使得，当沿着曲线行进时，法向量始终指向右手方向。
You know it's automatically OK because if you have a closed curve, then the vector field is, I mean, if a vector field is defined on the curve it will also be defined inside.
它必然成立，因为如果给出一条闭合曲线，然后向量空间是…，我是指，向量空间在曲线上有定义，当然在区域内部也有定义。
What we will do is just, at every point along the curve, the dot product between the vector field and the normal vector.
我们要做的是，沿着曲线的每一点上，取向量场和法向量的点积。
It measures how much a vector field goes across the curve.
它度量有多少向量场穿过了曲线。
We had a curve in the plane and we had a vector field.
平面上有一曲线，且存在着向量场。
Then actually there are ways you can use basically differentials and constrained partials to figure out what the tangent vector to the curve is and so on.
然后，可以用微分关系,或受约束的偏微分来表示,曲线的切向量，就是这样了。
Let's say that I have a plane curve and a vector field in the plane.
有一条平面曲线和这个平面上的向量场。
And, in some cases, for example, if you know that the vector field is tangent to the curve or if a dot product is constant or things like that then that might actually give you a very easy answer.
例如，在某些情况下，如果已知向量场与曲线相切，或者内积是一个常数等等，那么结果将会很简单。
But, if you have, so, again, the argument would be, well, if a vector field is defined on the curve, it's also defined inside.
问题的关键在于，如果一个向量场在曲线上有定义，内部也有定义。
And we looked at the component of a vector field in the direction that was normal to the curve.
我们研究的是，向量场在曲线法向量方向的情况。
So, I'm going to draw it in red. OK, so that's a unit vector that goes along the curve, and then the actual velocity is going to be proportional to that.
现在画成红色，这就是，沿曲线的单位速度向量，实际中的速度向量与它成比例的。
And that measured how much the vector field was going across the curve.
它度量了向量场穿过曲线的量。
So, the velocity vector is going to be always tangent to the curve.
速度向量总是与曲线相切的。
So, in both cases, we need the vector field to be defined not only, I mean, the left hand side makes sense if a vector field is just defined on the curve because it's just a line integral on c.
了解这两种表述后，我们不仅需要向量场，就是左边这里，这是曲线c上的线积分，向量场在曲线上有定义。
So, to say that a vector field with conservative means 0 that the line integral is zero along any closed curve.
一个保守的向量场就是说,沿任意闭曲线的线积分的结果是。
That means a vector that is at every point of the curve perpendicular to the curve and has length one.
也就是，曲线每一点上,垂直于曲线，模长为1的向量。
I have a curve in the plane and I have a vector field.
这有一条平面曲线和一个向量场。
That is my curve and my vector field.
那就是曲线和向量场。
What if I give you a really complicated curve and then you have trouble finding the normal vector?
如果给你的是，一条很复杂的曲线，而又找不到法向量？
But it could be that, well, imagine that my vector field accidentally goes in the opposite direction then this part of the curve, while things are flowing to the left, contributes negatively to flux.
的确有可能出现往两个方向流动的情况，可以想象到，这一小部分往相反方向流动，当流体向左流时，就只能算作负值了。
Then, if you had a flat disk with the curve going counterclockwise, the normal vector would go up.
就会得到一个被逆时针曲线包围的圆盘，法向量向上。
Well, if you followed what we've done there, you know that the normal vector compatible with this choice for the curve C is the one that points up.
如果一步一步的把该做的都做了，你会知道，与C相容的法向量,是向上的。
That is how we reformulated it. That means we take our curve and we figure out at each point how big the tangent component I guess I should probably take the same vector field as before.
这是另一种形式，它意味着,要求出每点处向量在切向量方向的分量,我还是用之前那个向量场吧。
Vector graph mesh model is a basic representation type of a body, particularly it is the most effective presentation method to representation complex body with curve and surface .
矢量图形网格模型是实体的一种基本表示形式，特别对于描述具有复杂曲线曲面的实体可以说是一种最有效的表达方法。
So, one of them says the line integral for the work done by a vector field along a closed curve counterclockwise is equal to the double integral of a curl of a field over the enclosed region.
其中一种说明了，在向量场上，沿逆时针方向，向量做的功等于，平面区域上旋度F的二重积分。
So if you've done the problem sets and found the same answers that I did, 0 then you will have found that this vector field had curve zero everywhere.
如果你们做了习题集,发现了和我一样的答案，你就会发现向量场的旋度在曲线上处处为。
Under Galilean transformations, expressions of Veloeities and accelerations in vertical curve Coordinates are derived by the ingenious use of Zero Vector and means of matrix.
在伽例略变换下，巧妙利用零矢量，给出了任意正交曲线坐标系中质点速度和加速度的矩阵表式方法。
Any regular curve that can be expressed by the vector parameter equation may be interpolated by this method.
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。
A new algorithm for modeling regression curve is put forward in the paper, it combines B-spline network with improved support vector regression.
将改进的支持向量回归机与B -样条网络相结合，提出了一种建立回归曲线模型的新算法。
The ideal fast starting curve of AC vector control system is presented according to the starting principle of DC speed regulating system.
根据直流调速系统的起动原理，给出了交流矢量控制系统的理想快速起动曲线。
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