The threshold is called theta.

阈值称为theta。

theta, y=1, else y=0.

当 a >=theta 时 y=1，反之 y=0。

So there's no restriction on theta.

在θ上没有限制。

With the chain rule, gives me a theta dot.

根据链式法则，我得到θ点。

Notice it's no longer even a function of theta.

注意，它不再是,关于θ的函数。

But, we have the constraint, a equals b cosine theta.

但是我们有约束条件，a=b*cosθ

R Now, v equals omega R, R so that equals theta dot times R.

现在v等于ω,即等于θ点乘以。

So, that means what you're doing is you're fixing the value of theta.

就是说，要做的是固定θ的值。

Well, we do that by figuring out how b depends on theta when a is fixed.

,算出了b是在a不变的情形下，它是怎样依赖于θ？

Plus the potential energy, which is mg times R times one minus cosine theta.

加上势能，也就是mg乘以R乘以,1/cosθ

This number can be larger than zero >0 if the sine theta is larger than zero.

这个数字可以大于,只要sinθ

dxdy Last time I told you if we have dx dy we could switch it to r dr d theta.

上一次课提到，如果给出,我们可以把它转换为rdrdθ

The two flips out, which eats up this two, so I get mg R and then I get a theta.

这两个没用了，被抵消，所以得到mgR和θ

If now we want to know what f prime is, f v/c plus v over c times the cosine of theta.

若想知道f撇的大小，撇等于f乘以1，then，f，prime，equals，f，times，one,加上,乘以cosθ

Now we forced this potential energy... we forced it into being dependent on theta squared.

现在我们使得势能。,我们强迫它,随着θ的平方而变。

So we get 2gl times the sine of theta mu k*cos 2 and the whole thing to the power one-half.

所以我们得到2gl*sinθ,θ，minus，mu，of，k，times，the，cosine，of，theta,所有项除以。

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。

Since there is no acceleration in the y direction, the normal force must be also mg cosine theta.

既然在y方向上,没有加速度，法向力也等于mgcosθ

The velocity of that object as a function of theta is given Rd And I can make you see that very easily.

物体的速度,和θ的关系是,θ/dt，by，R，d，theta/dt。,我可让你们简单得看。

Then this is the component in your direction we call that the radial component which is v cosine theta.

这是y方向的，组成因素,我们称之为辐射组成,等于vcosθ

R And the track has a radius R, and at this moment in time the angle equals theta, and here is the object.

轨道半径是，在这个时刻,角度等于θ,这是物体。

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。

This is a constant, and so you're going max to get theta equals theta maximum times the cosine omega t plus phi.

这是不变的,所以得到θ=θ,乘以cosωt+π

So it is this component, v cosine theta - which we call the radial velocity-- that is minus 100 kilometers per second.

这个成分，是vcosθ,我们叫做径向速度-,等于-100，公里每秒。

Meanwhile, the anti-X particle decays either to an antineutron or to two "hidden" antiparticles: anti-Y and anti-theta.

同时，一个反“X”粒子要么衰变成一个反中子，要么衰变成两个未知的粒子：反“Y”粒子和反“θ”粒子。

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。

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。

Or, the other way around, I have a function of x and y and I want to express it in terms of the polar coordinates r and theta.

反过来，有一个关于x和y的函数,也可以表示成极坐标r和θ

So, it is possible to treat -1 as a constant input whose weight, theta, is adjusted in learning, or, to use the technical term, training.

所以，我们可以把 -1 看成一个常量输入，它的权系数 theta 在学习（或者用技术术语，称为 培训）的过程中进行调整。