Rascunho Tcc2
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D = :Hx, yL Ε R2 - a < x < a e -
P@x__, y__D := H * CosB
In[8]:=
a2
Hà à
-a -
11-
x2 a2
x2
1 Π
CosB
x2
y2 +
a2
2
b2
1a2
>
F
x2 1-
x2 ,
1-
a2
a2
>F
F ây âx
a2
Pi In[2]:=
b2
IntegrateBP@x, yD, 8x, - a, a<, :y, -
a
Out[8]=
y2 +
2
x2 < y <
a2
x2
Pi In[1]:=
x2 1-
x2
ManipulateBPlot3DBH * CosB
y2 +
2
a2
b2
F, 8x, - a, a<, 8y, - b, b<, BoxRatios ® AutomaticF,
8a, .00000001, 100<, 8b, .0000000001, 100<, 8H, - 100, 0
a
40 20
48.9 0
b -20
38.8
-40
H 20
-44.2 0 Out[2]=
-20
-40 -50
0
50
P@x__, y__D := H CosB In[3]:=
In[9]:= Out[9]=
1 2
Π
x2 a2
g@u__, v__D := 8x, y< 8x, y< = 8a * u, b * v< 8a u, b v<
+
y2 b2
F
2
Notebook.nb
In[5]:=
88D@x, uD, D@y, uD<, 8D@x, vD, D@y, vD<< MatrixForm
Out[5]//MatrixForm=
K
In[6]:=
a 0 O 0 b
Jg = DetBK
a 0 OF 0 b
Out[6]=
ab
In[10]:=
IntegrateBP@x, yD * Jg, 8u, - 1, 1<, :v, abHà à 1
Out[10]=
-1 -
1-u2
1 Π
CosB 1-u2
2
1 - u2 ,
1 - u2 >F
u2 + v2 F â v â u
u2 + v2 = 1
In[11]:=
h@r__, Θ__ D := 8u, v<
In[12]:=
8u, v< = 8r * Cos@ΘD, r * Sin@ΘD<
Out[12]= In[13]:=
8r Cos@ΘD, r Sin@ΘD< 88D@u, rD, D@v, rD<, 8D@u, ΘD, D@v, ΘD<< MatrixForm
Out[13]//MatrixForm=
K
In[14]:= Out[14]= In[15]:= Out[15]= In[16]:= Out[16]=
Cos@ΘD Sin@ΘD O - r Sin@ΘD r Cos@ΘD
Det@%D r Cos@ΘD2 + r Sin@ΘD2 %=r r Jh = r r
Notebook.nb
In[18]:=
Integrate@P@x, yD * Jg * Jh, 8r, 0, 1<, 8Θ, 0, 2 Π
Out[18]=
Π In[20]:=
Clear@x, y, u, vD
In[22]:=
IntegrateB1, 8x, - a, a<, :y, - b
Out[22]=
abΠ Out@18D
In[23]:=
Out@22D
4 H H- 2 + ΠL
Out[23]=
Π2
x2 1-
x2 ,b
a2
1a2
>F
3
P@x__, y__D := H * CosB
In[8]:=
a2
Hà à
-a -
11-
x2 a2
x2
1 Π
CosB
x2
y2 +
a2
2
b2
1a2
>
F
x2 1-
x2 ,
1-
a2
a2
>F
F ây âx
a2
Pi In[2]:=
b2
IntegrateBP@x, yD, 8x, - a, a<, :y, -
a
Out[8]=
y2 +
2
x2 < y <
a2
x2
Pi In[1]:=
x2 1-
x2
ManipulateBPlot3DBH * CosB
y2 +
2
a2
b2
F, 8x, - a, a<, 8y, - b, b<, BoxRatios ® AutomaticF,
8a, .00000001, 100<, 8b, .0000000001, 100<, 8H, - 100, 0
a
40 20
48.9 0
b -20
38.8
-40
H 20
-44.2 0 Out[2]=
-20
-40 -50
0
50
P@x__, y__D := H CosB In[3]:=
In[9]:= Out[9]=
1 2
Π
x2 a2
g@u__, v__D := 8x, y< 8x, y< = 8a * u, b * v< 8a u, b v<
+
y2 b2
F
2
Notebook.nb
In[5]:=
88D@x, uD, D@y, uD<, 8D@x, vD, D@y, vD<< MatrixForm
Out[5]//MatrixForm=
K
In[6]:=
a 0 O 0 b
Jg = DetBK
a 0 OF 0 b
Out[6]=
ab
In[10]:=
IntegrateBP@x, yD * Jg, 8u, - 1, 1<, :v, abHà à 1
Out[10]=
-1 -
1-u2
1 Π
CosB 1-u2
2
1 - u2 ,
1 - u2 >F
u2 + v2 F â v â u
u2 + v2 = 1
In[11]:=
h@r__, Θ__ D := 8u, v<
In[12]:=
8u, v< = 8r * Cos@ΘD, r * Sin@ΘD<
Out[12]= In[13]:=
8r Cos@ΘD, r Sin@ΘD< 88D@u, rD, D@v, rD<, 8D@u, ΘD, D@v, ΘD<< MatrixForm
Out[13]//MatrixForm=
K
In[14]:= Out[14]= In[15]:= Out[15]= In[16]:= Out[16]=
Cos@ΘD Sin@ΘD O - r Sin@ΘD r Cos@ΘD
Det@%D r Cos@ΘD2 + r Sin@ΘD2 %=r r Jh = r r
Notebook.nb
In[18]:=
Integrate@P@x, yD * Jg * Jh, 8r, 0, 1<, 8Θ, 0, 2 Π
Out[18]=
Π In[20]:=
Clear@x, y, u, vD
In[22]:=
IntegrateB1, 8x, - a, a<, :y, - b
Out[22]=
abΠ Out@18D
In[23]:=
Out@22D
4 H H- 2 + ΠL
Out[23]=
Π2
x2 1-
x2 ,b
a2
1a2
>F
3
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