Now what I want to find actually V is what are these two vectors let 's call them U and V that correspond to moving a bit in the x direction or in the y direction ?

现在我实际上想知道的是，这两个向量是什么，我们称它们为，U和，两者对应的是 x 方向和y方向一点位移？

Ax which is the unit vector in the x direction y plus Ay y roof Z plus Az Z roof .

，乘以向量 x，Ax，times， x，roof，也就是 x 方向的单位矢量，加上Ay乘以向量，加上Az乘以向量。

The object will not be accelerated and the frictional force is going to adjust along the x direction so that the acceleration indeed is zero .

物体没有加速，摩擦力会沿 x 方向，调节自身大小，这样和速度为零。

Well I 'm going to decompose the tension into the y and into the x direction as we have done before .

分解这个张力，在y方向，和 x 方向，就像以前做的那样。

If you are here for example and you move in the x direction well you see as you get to there from the left the height first increases and then decreases .

如果你在这，往 x 方向 走，你看，从左边到这，高度首先增加了，然后下降了。

The motion is only in the x-axis along the x direction .

只在x轴，沿着 x轴的 方向进行移动。

That 's the same as indeed the partial derivatives in the x direction .

这和 x 方向 的 方向导数是一样的。

And now I have to know how the object moves in the x direction as a function of time and how it behaves as a function of time in the y direction .

现在我需要知道，物体在 x 轴 方向，随着时间是怎么移动的，以及在y轴方向，是怎么移动的。

We only deal with forces in the x direction that are of interest .

只需要关心 x 方向，即可。

These are the one-dimensional equations in x direction where there is no acceleration and the one-dimensional equations in the y direction where there is acceleration .

这些是 x 方向上的一维运动方程，在这个 方向上没有加速度，这些则是y方向上的一维运动方程，这个 方向上则有加速度。

So that 's the x direction .

这是 x 轴 方向。

It 's way smaller than the excursion in the x direction provided that your angle is small .

它比 x 方向的偏移，来得小，条件是这个角很小。

And that will decrease the speed & this component in the x direction .

这会让速度减慢-，在 x 方向的分力。

Now I can write down in the x direction Newton 's Second Law .

这就能在 x 方向，运用牛顿第二定律。

Unit vectors are always pointing in the direction of the positive axis x in the x direction is this one .

单位矢量，始终指向，轴的正方向，轴 方向的单位矢量，and，the， unit，vector，是这个。

And where we have this kind of a problem we will decompose it in two one-dimensional motions one in the x direction and one in the y direction .

当我们遇到这种问题时，我们将其分解为，两个一元运动问题，一个是在 x 方向，一个是在y轴方向。

So in fact what I 'm measuring here by the slope of the slice is the partial in the x direction .

事实上，我现在考察的斜率，就是 x 方向上的偏导。

So let 's write down now Newton 's Second Law in the x direction .

下面重写 x 方向的，牛顿第二定律。

There is no acceleration in the y direction only in x direction when it starts moving and that 's why we split it .

在y方向上没有加速度，只有在 x 方向上移动时才有，这就是分解它的原因。

So we have that du / dx equals minus F and I put the x there because-it 's a one-dimensional problem & it is only in the x direction .

我把x放那里，因为，这是个一维问题，它只是朝 着 x 方向-，负号是告诉你。

Let 's decompose that in y and x direction .

把它分解为 x和y 方向。

This is the increasing y direction and this is the increasing x direction .

这是y的正方向，而这是 x正 方向。

Now I want to do the same in the x direction for time t.

下面对在t时刻 x 方向的情况，做同样的分析。

The inertia terms and those relating to conduction in the X direction were also negligible .

惯性项和那些与 X 方向的导热有关的项也被略去。

Look at the excursion that this object made from equilibrium in the x direction .

看看这个，物体在 x 方向，离开平衡点的偏移。

Which could be pointing not just along the x direction but in general in all directions .

，不仅仅，沿着 x 方向，而是在所有方向。

There is no acceleration in the x direction .

因为 x 方向上没有加速度。

Second * Newton 's Second Law : ma this is the only force in the x direction .

根据牛顿第二定理：，等于。，ma，equals。。。，这是 x 方向的，唯一一个力。