转动惯量
探索涵盖包括转动惯量在内的刚体物理参数的新功能.
In[1]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_46.png)
wrench = ExampleData[{"Geometry3D", "Wrench"}, "Region"]
Out[1]=
![](assets.zh/moment-of-inertia/O_32.png)
选择一个点让扳手绕着它转.
In[2]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_47.png)
point = {-8, -0.168, 0};
In[3]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_48.png)
Show[wrench, Graphics3D[{PointSize[Large], Point[point]}],
ViewPoint -> {0, -\[Infinity], 0}]
Out[3]=
![](assets.zh/moment-of-inertia/O_33.png)
惯性矩阵的中心在此点上.
In[4]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_49.png)
\[ScriptCapitalI] = MomentOfInertia[wrench, point]
Out[4]=
![](assets.zh/moment-of-inertia/O_34.png)
找出主轴,也就是刚体趋向于围绕其转动的轴.
In[5]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_50.png)
principalaxes = Eigenvectors[\[ScriptCapitalI]]
Out[5]=
![](assets.zh/moment-of-inertia/O_35.png)
找出惯量椭球,其半径表示围绕主轴加速时所受的相对阻力.
In[6]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_51.png)
inertiaellipsoid = Ellipsoid[point, 1000 Inverse[\[ScriptCapitalI]]]
Out[6]=
![](assets.zh/moment-of-inertia/O_36.png)
图示扳手及其主轴和惯量椭球. 扳手手柄使得椭球沿其轴线伸长.
显示完整的 Wolfram 语言输入
In[8]:=
![Click for copyable input](assets.zh/moment-of-inertia/In_53.png)
Show[wrench, axes, BaseStyle -> Opacity[0.3]]
Out[8]=
![](assets.zh/moment-of-inertia/O_37.png)