So, there is a way to go from the unprimed coordinates to the prime coordinate by rotating your axis and actually calculating the components.

现在我们有一种方法可以从原坐标系,转变到新坐标系,只要旋转坐标轴,并实际地计算一下坐标即可

耶鲁公开课 - 基础物理课程节选

On the vertical axis I'll put two vertical axes in, just for the sake of things on the vertical axis I'll put my expected payoffs.

坐标系的纵轴,由于种种原因,我花了两个纵轴,纵轴表示我的预期收益

耶鲁公开课 - 博弈论课程节选

But you agree that there is no reason why somebody else couldn't come along and say, "You know what, I want to use a different set of axes.

但是你们得认识到,没有人会站出来说,"我想要用一套不同的坐标系

耶鲁公开课 - 基础物理课程节选

Here are the axes again.

再画一个坐标系。

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That was Cartesian space. When I plot r as a distance out from the nucleus that is sort of our simple-minded planetary model. Now let's look at energy.

笛卡尔坐标系，当我用r表示,离原子核的距离时，那只是我们头脑中简单的,类似行星的模型，现在我们看一下能量问题。

麻省理工公开课 - 固态化学导论课程节选

And similarly, actually, if we're looking at our polar coordinates here, what we see is it's any place where theta is equal to is what's going to put up on the x-y plane.

类似的，如果我们,看这里的极坐标系，我们能看到只要在theta等于,多少的地方就是ｘｙ平面。

麻省理工公开课 - 化学原理课程节选

The components come in the minute you pick your axis.

但它的分量由你所选择的坐标系确定

耶鲁公开课 - 基础物理课程节选

What I want to do is I want to draw a picture here, in which on the horizontal axis, I'm going to put the probability of the other guy choosing Right.

我要在这里画一张图,坐标系的横轴,表示对手选右的概率

耶鲁公开课 - 博弈论课程节选

Those directions are more natural for me."

这套坐标系对我来说更显得自然"

耶鲁公开课 - 基础物理课程节选

How do the components of A in the new rotated coordinate system relate to the components of the old coordinate system?

在旋转后的新坐标系中 A 的分量,和原始坐标系中 A 的分量有什么关联呢

耶鲁公开课 - 基础物理课程节选

You've got to be very used to the notion of taking a vector in some oblique direction and writing it in terms of i and j.

你们应该已经很熟悉,倾斜的坐标系中矢量的概念,和用 i 和 j 来表示该矢量的方法

耶鲁公开课 - 基础物理课程节选

For the simplest context in which one can motivate a vector and also motivate the rules for dealing with vectors, is when you look at real space, the coordinates x and y.

对于最简单的情况,我们能用矢量,以及相关的规则来处理的,是实空间,x-y 坐标系

耶鲁公开课 - 基础物理课程节选

I mentioned something of increasing importance only later, which is that you are free to pick another set of axes, not in the traditional x and y direction, but as an oblique direction.

后来我又讲了更重要的知识点,你可以随意选取另外一个坐标系,不再是传统的 x 和 y 方向,而是倾斜过的方向

耶鲁公开课 - 基础物理课程节选

For most of us, gravity acts this way, defines a vertical direction very naturally and the blackboard is oriented this way, so very natural to call that x and call that y and line up our axes.

对我们多数人来说,重力作用下,很自然地确定了竖直方向,而我们的黑板又是这个指向的,所以很自然地定出 x 轴和 y 轴,并标出我们的坐标系

耶鲁公开课 - 基础物理课程节选

I gave you a law of transformation of the components; namely, if the vector has components Ax and Ay in one reference frame and Ax prime and Ay prime in another reference frame, how are the two related?

我介绍过分量变换的法则,即如果矢量在一个坐标系的分量为 Ax 和 Ay,在另一坐标系中的分量为 Ax' 与 Ay',它们有着什么样的联系

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