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1

And then , you would be looking at a piece of that spherical shell corresponding to small values of phi and theta.

然后在这个夹壳中找出一小块，它跟 φ 和 θ 有关。

2

If an anti-Y particle collided with a proton, said proton would turn into a theta particle and a kaon.

如果用一个反 ”Y “粒子碰撞一个质子，该质子将衰变成一个 ”θ “粒子和一个 K 中介子。

3

So , I cannot ask myself just how will it change if I change theta and do random things with a and b ?

因此我无法提问下面这样的问题，如果我改变 θ ，同时对于 a 和 b 做随机的改变，它会怎样变化？

4

Of course , r goes all around the z axis , but I'm just doing a slice through one of these vertical half planes, fixing the value of theta.

当然，r 可以围绕 z 轴转圈，但我只做了一个垂直的半平面，对于一个确定的 θ 来说。

5

Well, you could call that the rate of change of theta with respect to theta with a constant .

你可以称之为，保持 a 不变，θ 关于 θ 自身的变化率。

6

What you will do is you will look for a given theta what are the bounds of r to be in the region .

你要做的是，在给定 θ 的情况下，找出这个区域 r 的上下限是什么。

7

And, because the equation does not involve theta, it's all the same if I rotate my vertical plane around the z axis .

由于等式没有包含 θ ，所以可以任意旋转这个垂直平面，绕着 z 轴。

8

And so you can express derivatives either in terms of x , y or in terms of r and theta with simple relations between them .

表示它的微分，要么用 x 和 y ，要么用 r 和 θ ，它们之间有简单的关系。

9

And, let's say that we want to understand how the area depends on theta.

这是一个关于 a，b ，θ 函数，我们想知道，面积是怎样依赖于 θ 的。

10

The goal is to see how things change when I change theta by a little bit .

我们的目标是来看看当我稍微改变 θ 时将会怎样变化。

11

Notice that when theta equals - if the object were here -- that you find that the u=mgR potential energy u equals mg R.

注意，当 θ ，如果物体在这里 -，你会发现，势能。

12

So , we set this to be zero . Theta, well, we are very happy because we want to express things in terms of theta.

所以我们令它等于零，很好，我们很高兴，因为我们就是想用 θ 来表示。

13

The next states , theta brainwaves, are typically of even greater amplitude and slower frequency .

下一个状态时 θ 脑电波，代表更大的振幅和更小的频率。

14

OK, and the corresponding angle is going to be measured by theta.

对应的角度是由 θ 决定的。

15

Let 's start with a simple example of an incline at an angle theta.

让我们以一个角度为，θ 的斜坡为例。

16

And this is always the same , independent of the angle of theta, because gravity is a conservative force .

它一直相同，和角度 θ 无关，因为重力是常量。

17

Say , polar coordinates . Let's say that I have a function but is defined in terms of the polar coordinate variables on theta.

比如说极坐标，有一个函数，是根据极坐标 θ 定义的。

18

This vector is uniquely determined in three-dimensional space so you should be able to find phi and theta.

这个矢量是在三维空间中，确定的，唯一的，因此你们可以求出 φ 和 θ

19

So we're going to get that theta double dot plus kappa times theta divided by Kappa, by the way, is the torsional constant .

所以我们会得到 θ 两点，+K*θ ，顺便说一下，K ，是扭力常数。

20

r Well, if I fix a value for theta, which means I chose an angle here, now I am shooting a ray from the origin in that direction .

的界限是什么呢？，What，are，the，bounds，for，r ？，固定 θ 的值，也就是在这取个角度，沿这个方向，由原点发出一条射线。

21

You cannot get the polar coordinates of a center of mass just by taking the average of R and the average of theta.

不能仅仅通过求 R 和 θ 的平均值，来得到重心的极坐标。

22

See, this is the same formula as the one over there , just dividing everything by partial theta and with subscripts little a .

这和那边的公式是一样的，只是通过偏 θ 和下标 a 把所有的事情分开，如果对你来说用这种方法更容易理解。

23

All right, let's suppose now that we increase the angle theta until the object starts to slide .

假设现在，我们扩大 θ 的角度，直到物体开始下滑。

25

And, differentiate the right-hand side as a function of b and theta.

把右边当成 b 和 θ 的函数来做微分。

26

It is common to just use plain text, often a single character, as the content of the Content MathML token element ci (theta in Listing 1 ).

只使用纯文本（通常是单个字符）作为 ContentMathML 记号元素 ci （清单 1 中的 θ ）的内容是很常见的做法。

27

And I remember when I last lectured 801, that was in 1993 , - I derived that in class -- T2 and T1 as a function of this angle theta.

我记得上一堂课，是在 1993年，我在课堂上推导了它 -，和 T1 之间 2，the，relation，between，T2 ，受 θ 影响的关系。

28

And let the velocity of the source I could put transmitter here , but we can drop that index and let this angle be theta.

使电磁辐射源的速度，我把发射机放这里，可以把指数下降，这是角度 θ

29

P And this is the moment of inertia about point P times alpha , and alpha is theta double dot .

点 P 的转动惯量，乘以 α ，现在 α 是 θ 两点。

30

OK, so in fact , what we found, if you want, is the rate of change of b with respect to theta.

实际上，我们所求出的，是 b 关于 θ 的变化率。

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