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]:=

wrench = ExampleData[{"Geometry3D", "Wrench"}, "Region"]

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选择一个点让扳手绕着它转.

In[2]:=

point = {-8, -0.168, 0};

In[3]:=

Show[wrench, Graphics3D[{PointSize[Large], Point[point]}], ViewPoint -> {0, -\[Infinity], 0}]

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惯性矩阵的中心在此点上.

In[4]:=

\[ScriptCapitalI] = MomentOfInertia[wrench, point]

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找出主轴，也就是刚体趋向于围绕其转动的轴.

In[5]:=

principalaxes = Eigenvectors[\[ScriptCapitalI]]

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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]:=

inertiaellipsoid = Ellipsoid[point, 1000 Inverse[\[ScriptCapitalI]]]

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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.

In[7]:=

axes = Graphics3D[{Opacity[1], Arrowheads[{-0.04, 0.04}], {Specularity[Gray, 10], Gray, inertiaellipsoid}, MapThread[{RGBColor[#2], Arrow[Tube[{point - 4 #, point + 4 #}, .06]]} &, {principalaxes, IdentityMatrix[3]}]}];

In[8]:=

Show[wrench, axes, BaseStyle -> Opacity[0.3]]

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