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Constructing a new function is very simple.
| In[36]:= weirdf[x_, y_] := If[x^2 + y^2 < 1, x^2 + y^2, Exp[1 - x^2 - y^2]] |
|
| The function which Plot3D requires must evaluate to a number. Thus our weird function is quite adequate. | In[37]:= Plot3D[weirdf[s, t], {s, -2, 2}, {t, -2, 2}] |
| Out[37]= - SurfaceGraphics - |
A further possibility is to use Mathematica numerical capabilities. For this the NDSolve function, which numerically solves differential equations, is very suitable.
| NDSolve returns an InterpolatingFunction. Of course we could have solved this problem analytically. | In[38]:= NDSolve[{x''[t] == -x[t], x[0] == 2, x'[0] == 0},
x, {t, 0, 20}] Out[38]= {{x -> InterpolatingFunction[{0., 20.}, <>]}} |
| This plots the result. Evaluate is necessary since Plot is HoldAll. | In[39]:= ParametricPlot3D[Evaluate[{t, x[t], D[x[t], t]} /. %],
{t, 0, 20}] |
| Out[39]= - Graphics3D - |
|
| This example is more complex. It comprises of two coupled oscillators. | In[40]:= NDSolve[{x''[t] == -x[t] - x[t] y[t]^2,
y''[t] == -y[t] - x[t] y[t]^2,
x[0] == 2, x'[0] == 0, y[0] == 1, y'[0] == 0},
{x, y}, {t, 0, 20}] Out[40]= {{x -> InterpolatingFunction[{{0., 20.}}, <>], y -> InterpolatingFunction[{{0., 20.}}, <>]}} |
| This shows the solution. | In[41]:= ParametricPlot3D[Evaluate[{t, x[t], y[t]} /.
First[%]], {t, 0, 20}] |
| Out[41]= - Graphics3D - |
| next page: 6.3 Animation | back to table of contents |