And, you switch it into spherical coordinates.

将这个方程转换到球坐标形式。

There we want to think a tiny bit about spherical coordinates again.

我们需要再次考虑球坐标。

But since spherical coordinates we have actually learned about something much more interesting,namely spherical coordinates.

但我们已经学习了更有意思的东西,即球坐标。

The Laplacian in the columnar and spherical coordinates is deduced by using the derivative principle of the multivariable functions.

使用多元复合函数微商法则，导出拉普拉斯算符在柱面坐标系和球面坐标系中表达式。

Spherical coordinates are a way of describing points in space in terms of three variables.

球坐标是一种用三个变量,表示空间中点的位置的方法。

This method is applied to a manipulator with spherical coordinates.

并将此方法应用到三自由度球坐标机械手上。

We have rectangular coordinates, we have cylindrical coordinates and we have spherical coordinates.

我们有直角坐标系，有柱坐标系和球坐标系。

That will give you a good idea of what kinds of things we've seen in spherical coordinates.

这将会给你一些,关于我们已经在球坐标中学过的东西的好的想法。

The variable or distance to the origin in spherical coordinates.

变量或是在球座标中距离原点的距离。

The helical surface equations of the spherical hob are set up in spherical coordinates. The formulas of the side clearance angle and numerical examples are given.

在球坐标系中，建立了球形滚刀的各个螺旋面方程，推导了侧后角公式，并给出了计算实例。

Now, it is OK to think of them as spherical coordinates, but I would like to encourage you not to think of them as spherical coordinates.

那么现在可以在球坐标上考虑了,但是我希望大家,不要把它们看做球坐标。

But let's do it in spherical coordinates because that's the topic of today.

但我们用球坐标来做,因为这才是今天的主题。

And, now we have to learn about spherical coordinates, which you will see are a lot of fun.

今天我们来学习下球坐标，这是个很有意思的东西。

By the method of linear transformation, the solution forms of vector wave equation in spherical coordinates, L, M and N, are transformed to the many other kinds of forms.

利用线性变换的方法，将球坐标下矢量波动方程解的形式L、M和N变换为其他多种形式。

So, what's the idea of spherical coordinates?

球坐标的定义是什么呢？

So, if you are asked to find the average distance from the origin, spherical coordinates can be interesting.

如果你想求到中心的平均距离，球坐标还是不错的。

And, of course, you will actually do that in spherical coordinates because it is easier that way.

当然也可以在球坐标中计算,而且那么做更简单。

So now we're going to triple integrals in spherical coordinates.

现在，在球坐标中进行三重积分。

Well, we have to figure out how to set up our triple integral in spherical coordinates.

先看看怎么,在球坐标中建立三重积分。

Now, there's also spherical coordinates.

现在，考虑球坐标。

So, it's much better to set up these integrals in spherical coordinates.

所以球坐标的优势就显现出来了。

One is applicable to the rectangular coordinates, and the other to the spherical coordinates.

其中一个适用于直角坐标，一个适用于球面坐标。

A new motion model with a tracking algorithm is introduced in this paper to track a maneuvering target such as a sea skimming anti ship cruise missile (ASCM) in spherical coordinates.

这个新的模型着重于对球坐标系中目标运动模式和加速度非线性关系的深入分析。

OK, let's see, who had seen spherical coordinates before just to see?

我看看，谁曾经学过球坐标么？

By using the primitive equations of motion in spherical coordinates, free oscillations of the atmosphere are discussed.

利用球坐标中的原始运动方程组，讨论了大气的自由振动问题。

SVD is processed in a 2D mapping grid, which is produced by vertex's spherical coordinates and has similarly local statistical property of original mesh.

奇异值分解在与网格模型几何数据局部统计特征相似的球面坐标映射方阵中进行，水印序列嵌入到方阵生成的奇异值序列中。

And, I mean, there's a fairly small list of kinds of surfaces that we've seen how to set up in spherical coordinates.

我们已经知道,一部分曲面是如何建立球坐标的。

So, in fact, it simplifies quite a bit if you do it in spherical coordinates.

事实上用球坐标,简化了式子。

And now,we're going to try to find the volume of that spherical cap again but using spherical coordinates instead.

现在来求下被切出的球冠的体积,我们用球坐标来求。

OK, so note how the equation of this horizontal plane in spherical coordinates has become a little bit weird.

球坐标下的平面方程,看上去有点诡异。