Moment of Inertia
Explore new capabilities covering physical parameters of a rigid body, including rotational inertia.
In[1]:=
![Click for copyable input](assets.en/moment-of-inertia/In_46.png)
wrench = ExampleData[{"Geometry3D", "Wrench"}, "Region"]
Out[1]=
![](assets.en/moment-of-inertia/O_32.png)
Pick a point for the wrench to rotate about.
In[2]:=
![Click for copyable input](assets.en/moment-of-inertia/In_47.png)
point = {-8, -0.168, 0};
In[3]:=
![Click for copyable input](assets.en/moment-of-inertia/In_48.png)
Show[wrench, Graphics3D[{PointSize[Large], Point[point]}],
ViewPoint -> {0, -\[Infinity], 0}]
Out[3]=
![](assets.en/moment-of-inertia/O_33.png)
The inertia matrix centered at this point.
In[4]:=
![Click for copyable input](assets.en/moment-of-inertia/In_49.png)
\[ScriptCapitalI] = MomentOfInertia[wrench, point]
Out[4]=
![](assets.en/moment-of-inertia/O_34.png)
Find the principal axes, the axes a body tends to rotate about.
In[5]:=
![Click for copyable input](assets.en/moment-of-inertia/In_50.png)
principalaxes = Eigenvectors[\[ScriptCapitalI]]
Out[5]=
![](assets.en/moment-of-inertia/O_35.png)
Find the inertia ellipsoid whose radii indicate the relative resistance to accelerate about a principal axis.
In[6]:=
![Click for copyable input](assets.en/moment-of-inertia/In_51.png)
inertiaellipsoid = Ellipsoid[point, 1000 Inverse[\[ScriptCapitalI]]]
Out[6]=
![](assets.en/moment-of-inertia/O_36.png)
Show the wrench with its principal axes and inertia ellipsoid. The wrench arm stretches the ellipsoid along its axis.
show complete Wolfram Language input
In[8]:=
![Click for copyable input](assets.en/moment-of-inertia/In_53.png)
Show[wrench, axes, BaseStyle -> Opacity[0.3]]
Out[8]=
![](assets.en/moment-of-inertia/O_37.png)