Rascunho Tcc2

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