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NdSolve::ndnum error and Polar Coordinates plot

Posted 11 years ago
Hello,
I'm trying to solve the system of differential equations in polar coordinates and after that plot this solution.
The system is










Here is the code
 c = 100;
 b = 1;
 a = 0.99;
 w = NDSolve[{r'[t] ==
     r[t]*(Cos[tet[t]]^2 + a*Sin[tet[t]]^2) -
      c*r[t]^2*Sin[tet[t]]*Cos[tet[t]]*(Cos[tet[t]] - a*Sin[tet[t]]) -
      r[t]^2*(Cos[tet[t]]^3 + a*b*Sin[tet[t]]^3),
      tet'[t] == (a - 1)*Sin[tet[t]]*Cos[tet[t]] -
      c*r[t]*Sin[tet[t]]*Cos[tet[t]]*(a*Cos[tet[t]] - Sin[tet[t]]) -
     r[t]*Sin[tet[t]]*Cos[tet[t]]*(a*b*Sin[tet[t]] - Cos[tet[t]]),
     r[0] == 0, tet[0] == 0}, {r[t], tet[t]}, {t, 0, 1000}]


How to plot this solution on polar plot?
I tried use ParametricPlot, PolarPlot and ListPolarPlot - no results

Thanks for help.

Best regards, 
Danila
POSTED BY: Danila Zharenkov
6 Replies
Thank  you, yes, I found some  mistakes in math model.
POSTED BY: Danila Zharenkov
With the given parameters and initial conditions, r and tet are always zero.
 In[1]:= c = 100;
 b = 1;
 a = 0.99;
 w = NDSolve[{r'[t] ==
     r[t]*(Cos[tet[t]]^2 + a*Sin[tet[t]]^2) -
      c*r[t]^2*Sin[tet[t]]*Cos[tet[t]]*(Cos[tet[t]] - a*Sin[tet[t]]) -
      r[t]^2*(Cos[tet[t]]^3 + a*b*Sin[tet[t]]^3),
    tet'[t] == (a - 1)*Sin[tet[t]]*Cos[tet[t]] -
      c*r[t]*Sin[tet[t]]*Cos[tet[t]]*(a*Cos[tet[t]] - Sin[tet[t]]) -
     r[t]*Sin[tet[t]]*Cos[tet[t]]*(a*b*Sin[tet[t]] - Cos[tet[t]]), r[0] == 0,
   tet[0] == 0}, {r[t], tet[t]}, {t, 0, 1000}]

Out[4]= {{r[t] -> InterpolatingFunction[][t], tet[t] -> InterpolatingFunction[][t]}}

        (* This samples only every 100th point.  All 1001 were zero.  *)
In[5]:= Table[ Evaluate[{r[t], tet[t]} /. w[[1]]], {t, 0, 1000, 100}]

Out[5]= {{0., 0.}, {0., 0.}, {0., 0.}, {0., 0.}, {0., 0.}, {0., 0.}, {0., 0.},
   {0., 0.}, {0., 0.}, {0., 0.}, {0., 0.}}

     (*  r' and  tet'  are zero at the beginning, and it looks like they
          never get the chance to grow.  *)
In[6]:= Eliminate[{r'[t] ==
    r[t]*(Cos[tet[t]]^2 + a*Sin[tet[t]]^2) -
     c*r[t]^2*Sin[tet[t]]*Cos[tet[t]]*(Cos[tet[t]] - a*Sin[tet[t]]) -
     r[t]^2*(Cos[tet[t]]^3 + a*b*Sin[tet[t]]^3),
   tet'[t] == (a - 1)*Sin[tet[t]]*Cos[tet[t]] -
     c*r[t]*Sin[tet[t]]*Cos[tet[t]]*(a*Cos[tet[t]] - Sin[tet[t]]) -
     r[t]*Sin[tet[t]]*Cos[tet[t]]*(a*b*Sin[tet[t]] - Cos[tet[t]]), r[0] == 0,
   tet[0] == 0} /. t -> 0, {r, tet}]

Out[6]= r[0] == 0. && tet[0] == 0. && r'[0] == 0. &&
  100. tet'[0] == -1. Cos[tet[0]] Sin[tet[0]]

In[7]:= FullSimplify[%]
Out[7]= r[0] == 0 && tet[0] == 0 && r'[0] == 0 && tet'[0] == 0
POSTED BY: Bruce Miller
Could you please first edit your post and correct syntax of your code?
POSTED BY: Vitaliy Kaurov
Of course, sorry.
Post was edited.
POSTED BY: Danila Zharenkov
Ohh, thanks. My fault.

I tried to use PolarPlot as I wrote above, but no results.
Can you give some advice how to plot this solution?
POSTED BY: Danila Zharenkov
Built-in functions in Mathematica start with capital letters.   Sin and Cos.
POSTED BY: Bruce Miller
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