
球面坐标
And, you switch it into spherical coordinates.
将這個方程轉換到球坐标形式。
There we want to think a tiny bit about spherical coordinates again.
我們需要再次考慮球坐标。
But since spherical coordinates we have actually learned about something much more interesting,namely spherical coordinates.
但我們已經學習了更有意思的東西,即球坐标。
The Laplacian in the columnar and spherical coordinates is deduced by using the derivative principle of the multivariable functions.
使用多元複合函數微商法則,導出拉普拉斯算符在柱面坐标系和球面坐标系中表達式。
Spherical coordinates are a way of describing points in space in terms of three variables.
球坐标是一種用三個變量,表示空間中點的位置的方法。
This method is applied to a manipulator with spherical coordinates.
并将此方法應用到三自由度球坐标機械手上。
We have rectangular coordinates, we have cylindrical coordinates and we have spherical coordinates.
我們有直角坐标系,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.
這将會給你一些,關于我們已經在球坐标中學過的東西的好的想法。
The variable or distance to the origin in spherical coordinates.
變量或是在球座标中距離原點的距離。
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,建立了球形滾刀的各個螺旋面方程,推導了側後角公式,并給出了計算實例。
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.
那麼現在可以在球坐标上考慮了,但是我希望大家,不要把它們看做球坐标。
But let's do it in spherical coordinates because that's the topic of today.
但我們用球坐标來做,因為這才是今天的主題。
And, now we have to learn about spherical coordinates, which you will see are a lot of fun.
今天我們來學習下球坐标,這是個很有意思的東西。
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.
利用線性變換的方法,将球坐标下矢量波動方程解的形式L、M和N變換為其他多種形式。
So, what's the idea of spherical coordinates?
球坐标的定義是什麼呢?
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離,球坐标還是不錯的。
And, of course, you will actually do that in spherical coordinates because it is easier that way.
當然也可以在球坐标中計算,而且那麼做更簡單。
So now we're going to triple integrals in spherical coordinates.
現在,在球坐标中進行三重積分。
Well, we have to figure out how to set up our triple integral in spherical coordinates.
先看看怎麼,在球坐标中建立三重積分。
Now, there's also spherical coordinates.
現在,考慮球坐标。
So, it's much better to set up these integrals in spherical coordinates.
所以球坐标的優勢就顯現出來了。
One is applicable to the rectangular coordinates, and the other to the spherical coordinates.
其中一個適用于直角坐标,一個適用于球面坐标。
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.
這個新的模型着重于對球坐标系中目标運動模式和加速度非線性關系的深入分析。
OK, let's see, who had seen spherical coordinates before just to see?
我看看,誰曾經學過球坐标麼?
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運動方程組,讨論了大氣的自由振動問題。
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.
奇異值分解在與網格模型幾何數據局部統計特征相似的球面坐标映射方陣中進行,水印序列嵌入到方陣生成的奇異值序列中。
And, I mean, there's a fairly small list of kinds of surfaces that we've seen how to set up in spherical coordinates.
我們已經知道,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.
事實上用球坐标,簡化了式子。
And now,we're going to try to find the volume of that spherical cap again but using spherical coordinates instead.
現在來求下被切出的球冠的體積,我們用球坐标來求。
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,看上去有點詭異。
球坐标系(Spherical Coordinates)是三維空間中描述點位置的一種坐标系統,尤其適用于具有球對稱性的問題。它通過三個參數确定點的位置:
半徑(r)
表示點與原點(坐标中心)的直線距離,範圍是 ( r geq 0 )。
極角(θ,theta)
也稱為“天頂角”,是點與正z軸之間的夾角,範圍是 ( 0 leq theta leq pi )。當 ( theta = 0 ) 時,點位于z軸正方向;( theta = pi ) 時位于z軸負方向。
方位角(φ,phi)
點在xy平面上的投影與正x軸的夾角,範圍是 ( 0 leq phi < 2pi )。類似于極坐标系中的角度。
球坐标 ((r, theta, phi)) 轉換為直角坐标 ((x, y, z)) 的公式為:
$$
x = r sintheta cosphi
y = r sintheta sinphi
z = r costheta
$$
如果需要進一步了解具體應用或公式推導,可以參考數學或物理教材中的“坐标系轉換”章節。
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