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1·There are three methods for tangent vector discussed in this paper.

本文指出了切线向量的三种求法。

2·The purely kinematical equation for the tangent vector of a line element is derived.

导出了线元切向量的变形方程以及拉伸轴在极射赤面投影图上位置变化计算公式。

3·In this paper, the tangent vector loading method and the boundary element restrain method was presented.

采用了切线矢量加载和边界单元的约束方法建立分析模型。

4·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。

5·Then, if I choose any vector in that tangent plane.

那么如果我选择了任何位于切平面的向量。

6·We know that the gradient is perpendicular to this vector that's tangent to the level surface What about other vectors tangent to the level surface?

我们知道梯度向量垂直于这个向量，而速度向量是相切于等值面的，其他相切于等值面的向量，又如何呢？

7·It has a hat because it's a unit vector, and t because it's tangent.

这上面有一个帽子表示它是单位矢量，T表示它是切线。

8·OK, and that's going to be the normal vector to the surface or to the tangent plane.

这就是切平面的，或者说这个曲面的法向量。

9·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。

10·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。