Hauptachsentrafo - Testrechnung

In[]:=
A={{2,0,1},{0,1,1},{1,1,1}}
Out[]=
{{2,0,1},{0,1,1},{1,1,1}}
In[]:=
MatrixForm[A]
Out[]//MatrixForm=
2
0
1
0
1
1
1
1
1
In[]:=
principalAxisMat[A]
Output result...
Out[]=
{1,0,0},
5
8
,
1
2
,-
1
2
,-
9
8
,
1
2
,
1
2
,0,0,
1
2
,{0,2,0},
1
2
,0,0
In[]:=
A2={{4,4,1},{4,5,-1},{1,-1,2}}
Out[]=
{{4,4,1},{4,5,-1},{1,-1,2}}
In[]:=
MatrixForm[A2]
Out[]//MatrixForm=
4
4
1
4
5
-1
1
-1
2
In[]:=
principalAxisMat[A2]
Output result...
Out[]=
{1,0,0},-1,-
3+
13
26+6
13
,
-3+
13
26-6
13
,-1,
2
13+3
13
,
1
2
+
3
2
13
,{-1,0,0},0,
1
2
(7+
13
),0,0,0,
1
2
(7-
13
)
In[]:=
N[%]
Out[]=
{{{1.,0.,0.},{-1.,-0.957092,0.289784},{-1.,0.289784,0.957092}},{{-1.,0.,0.},{0.,5.30278,0.},{0.,0.,1.69722}}}
In[]:=
A30={{0,0,0},{0,2,0},{0,0,5}}
Out[]=
{{0,0,0},{0,2,0},{0,0,5}}
In[]:=
T30={{1,0,0},{3,Cos[α],-Sin[α]},{-5,Sin[α],Cos[α]}}/.α->π/5
Out[]=
{1,0,0},3,
1
4
(1+
5
),-
5
8
-
5
8
,-5,
5
8
-
5
8
,
1
4
(1+
5
)
In[]:=
A3=Transpose[T30].A30.T30//Simplify
Out[]=
143,
1
4
6+6
5
-25
10-2
5
,-3
1
2
(5-
5
)
-
25
4
(1+
5
),
1
4
6+6
5
-25
10-2
5
,
1
8
(31-3
5
),
3
8
1
2
(5-
5
)
(1+
5
),-3
1
2
(5-
5
)
-
25
4
(1+
5
),
3
8
1
2
(5-
5
)
(1+
5
),
1
8
(25+3
5
)
In[]:=
{T3,B3}=principalAxisMat[A3]
Switch command reached.
Solving equations...
Out[]=
$Aborted