Message Boards Message Boards

0
|
5214 Views
|
7 Replies
|
3 Total Likes
View groups...
Share
Share this post:

How to plot the Joukowski curve...?

Posted 9 years ago
POSTED BY: Simon Cadrin
7 Replies
POSTED BY: Simon Cadrin
POSTED BY: Frank Kampas

enter image description here

POSTED BY: Simon Cadrin
In[1]:= a = 2;

In[2]:= b[t_] = 3/10 + I + 5/2 Exp[I t];

In[3]:= z[t_] = 1/2 (b[t] + a^2/b[t])

Out[3]= 1/2 ((3/10 + I) + (5 E^(I t))/2 + 
   4/((3/10 + I) + (5 E^(I t))/2))

In[7]:= reimz[t_] = {Re[z[t]], Im[z[t]]} // ComplexExpand // 
  FullSimplify

Out[7]= {1/
  20 (3 + 25 Cos[t]) (1 + 200/(367 + 75 Cos[t] + 250 Sin[t])), -(1/
   2) + (5 Sin[t])/4 + (267 + 75 Cos[t])/(
  367 + 75 Cos[t] + 250 Sin[t])}

In[12]:= dz[t_] = D[reimz[t], t] // FullSimplify

Out[12]= {-((
   250 (3 + 25 Cos[t]) (10 Cos[t] - 3 Sin[t]))/(367 + 75 Cos[t] + 
     250 Sin[t])^2) - 
  5/4 Sin[t] (1 + 200/(367 + 75 Cos[t] + 250 Sin[t])), 
 5/4 (Cos[t] - (
    600 (25 + 89 Cos[t] + 10 Sin[t]))/(367 + 75 Cos[t] + 
      250 Sin[t])^2)}

In[16]:= NIntegrate[Sqrt[dz[t].dz[t]], {t, 0, 2 \[Pi]}]

Out[16]= 9.40235
POSTED BY: Frank Kampas

How to calculate the circumference of the curve?

POSTED BY: Simon Cadrin
POSTED BY: Simon Cadrin
POSTED BY: Frank Kampas
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract