It is pointed out that the translation potential energy of the dipole can be defined even if in the curl field.
文章还指出在有旋场中也可以定义偶极子的平动势能。
Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
The curl of a vector field in space is actually a vector field, not a scalar function. I have delayed the inevitable.
空间中的向量场的旋度，是一个向量场，而不是一个标量函数，我必须告诉你们。
That other field is given from the first one just by taking its curl So, after you take the curl, you obtain a different vector field.
另一个向量场，是通过计算第一个向量场的旋度得到的，计算旋度之后，就可以得到一个不同的向量场。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
See, if your field was conservative — 0 if a curl was zero then the right-hand side would just be zero.
如果场是保守的-，如果旋度是0，那么右手边的结果也会是。
That is called the curl of a vector field.
这个量叫向量场的旋度。
OK, so let's assume that we have a vector field whose curl is zero.
假设有一个旋度为零的向量场。
In fact, the curl of the field is one, one, one.
实际上，场的旋度是。
And that would be fortunate because if a curl is zero then your field is less conservative.
真是十分幸运啊，因为如果旋度是0，那么场至少是保守的。
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。
There is another thing that we know because if a force derives from a potential 0 then that means its curl is zero Thats the criterion we have seen for a vector field to derive from a potential.
我们还知道,如果力是由势产生的,那么其旋度是,这就是我们得到的,关于从势产生的向量场的准则。
In particular, a force field with no curl is a force field that does not generate any rotation motion.
特别地，一个没有旋度的力场，就是一个不产生任何旋转运动的力场。
More about curl.If we have a velocity field, then we have seen that the curl measures the rotation affects.
关于旋度的更多介绍，设有一速度场，我们知道旋度是测量旋转影响的。
Now, an important difference between curl here and curl in the plane is that now the curl of a vector field is again a vector field.
和平面上的旋度的一个重要的不同点是，这里向量场的旋度，仍然是一个向量场。
If you have a small solid somewhere, the curl will just measure how much your solid starts spinning if you leave it in this force field.
假如力场中某处有一小块固体，旋度度量的是固体在力场中的旋转程度，在力场里来观察。
And that is indeed going to be the curl of F. in practice, if you have to compute the curl of a vector field, you know, don't try to remember this formula.
这就是F的旋度，在实际应用中，如果你必须计算一个向量场的旋度，不要尝试记忆这个公式。
And the last one tells you how the curl of the magnetic field is caused by motion of charged particles.
最后一个说明了，磁场的旋度，是如何由电荷的运动产生的。
Concretely, if you imagine that you are putting something in there, you know, if you are in a velocity field the curl will tell you how fast your guy is spinning at a given time.
具体来讲，想象一下，你要放东西在那里，如果是在一速度场内，旋度告诉你，在给定的时间他旋转的速度。
The question is what does the curl of a force field mean?
问题是一个力场的旋度代表什么？
That one tells you about the curl of the electric field.
那个关于电场旋度的方程。
And the curl of the electric field will generate voltage between these two guys.
电场的旋度，在二者间产生了电压。
And the curl of a force field tells you how quickly the angular velocity is going to increase or decrease. OK.
力场的旋度告诉你，角速度增加或减小的快慢。
If the curl is zero, and if the field is defined everywhere, then it's going to be conservative.
如果旋度为0，而且场处处有定义，那么它就是保守场。
The test that we saw last time saying, well, to check if something is a gradient field if it's conservative, 0 we just have to compute the curl and check whether it's zero.
由上次的测试可知，如果一个东西是保守的，要确定是不是梯度，我们只需要计算旋度，查看它是否是。
This field is proved to have both divergence and curl.
并证明该电场是有源有旋场。
This paper introduced the basic principle of air vortex spinning and laid stresses on curl flow field in the air vortex twister, and the collecting and taking off of link fiber in air vortex spinning.
介绍了涡流纺纱的基本原理，对涡流加拈器中旋转流场的形成、纤维环的凝聚与剥取做了重点阐述。
This paper introduced the basic principle of air vortex spinning and laid stresses on curl flow field in the air vortex twister, and the collecting and taking off of link fiber in air vortex spinning.
介绍了涡流纺纱的基本原理，对涡流加拈器中旋转流场的形成、纤维环的凝聚与剥取做了重点阐述。
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