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?
Let's decompose that in y and x direction. 把它分解为x和y方向。
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。
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。
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。
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。
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。
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。
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。
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。
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。
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。
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。
That is because there is only an acceleration in the y direction but the motion in the y direction is completely independent of the x direction. 这是因为加速度,只在y方向才有,而y方向的运动,与x方向的运动是相互独立的。
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。
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。
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。
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。
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。
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。
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。
There is no acceleration in the x direction. 因为x方向上没有加速度。
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。
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。
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。
We only deal with forces in the x direction that are of interest. 只需要关心x方向,即可。
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。
I have here a spray paint can which is suspended between two springs, and I can oscillate it vertically, which is your x direction, like that. 这是一个喷漆罐,挂在,两个弹簧之间,我让它垂直振荡,在x方向,像这样。
So that's the x direction. 这是x轴方向。
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。