# NdSolve::ndnum error and Polar Coordinates plot

Posted 10 years ago
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 Hello,I'm trying to solve the system of differential equations in polar coordinates and after that plot this solution.The system isHere 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 resultsThanks for help.Best regards, Danila
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Posted 10 years ago
 Thank  you, yes, I found some  mistakes in math model.
Posted 10 years ago
 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 10 years ago