? Solve
Solve@eqns, varsD attempts to solve an equation or set of equations
for the variables vars. Solve@eqns, vars, elimsD attempts to solve
the equations for vars, eliminating the variables elims. More…
Solve@8a ^ 2 ã 2 vc ^ 2 ê r ^ 2 - vc ^ 2 k ê r + k ^ 2 cs ^ 2<, kD
::k Ø -
- r vc2 - r
4 a2 cs2 r2 - 8 cs2 vc2 + vc4
2 cs2 r2
>, :k Ø -
- r vc2 + r
4 a2 cs2 r2 - 8 cs2 vc2 + vc4
2 cs2 r2
k ê. %2@@1DD
-
- r vc2 - r
4 a2 cs2 r2 - 8 cs2 vc2 + vc4
2 cs2 r2
k ê. %2@@2DD
-
- r vc2 + r
4 a2 cs2 r2 - 8 cs2 vc2 + vc4
2 cs2 r2
k1@r_, vc_, cs_, m_, w_D = %4 ê. a Ø Hm vc ê r - wL
- r vc2 - r
- 8 cs2 vc2 + vc4 + 4 cs2 r2 I
m vc
r
- wM
2
-
2 cs2 r2
k2@r_, vc_, cs_, m_, w_D = %5 ê. a Ø Hm vc ê r - wL
- r vc2 + r
- 8 cs2 vc2 + vc4 + 4 cs2 r2 I
m vc
r
- wM
2
-
2 cs2 r2
r1@vc_, m_, w_D = vc Hm - Sqrt@2DL ê w
J-
2 + mN vc
w
r2@vc_, m_, w_D = vc Hm + Sqrt@2DL ê w
J 2 + mN vc
w
r1@40, 2, 40 ê 10.D
5.85786
r2@40, 2, 40 ê 10.D
34.1421
Plot@k1@r, 40, 10, 2, 40 ê 10.D, 8r, r1@40, 2, 40 ê 10.D + .001, r2@40, 2, 40 ê 10.D - .001<D
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Hwrk3_13.nb
Plot@k2@r, 40, 10, 2, 40 ê 10.D, 8r, r1@40, 2, 40 ê 10.D + .001, r2@40, 2, 40 ê 10.D - .001<D
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f@r_, vc_, cs_, m_, w_D := NIntegrate@k1@z, vc, cs, m, wD, 8z, r1@vc, m, wD, r<D
Plot@f@r, 40, 10, 2, 40 ê 10.D, 8r, r1@40, 2, 40 ê 10.D + .001, r2@40, 2, 40 ê 10.D - .001<D
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? ParametricPlot
ParametricPlot@8fx, fy<, 8u, umin, umax<D produces a parametric plot of a curve with
x and y coordinates fx and fy generated as a function of u. ParametricPlot@88fx,
fy<, 8gx, gy<, ... <, 8u, umin, umax<D plots several parametric curves. More…
ParametricPlot@
8r * Cos@- f@r, 40, 10, 2, 40 ê 10.D ê 2D, r * Sin@- f@r, 40, 10, 2, 40 ê 10.D ê 2D<,
8r, r1@40, 2, 40 ê 10.D + .001, r2@40, 2, 40 ê 10.D - .001<, PlotStyle Ø 8RGBColor@1, 0, 0D<D
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ParametricPlot@
8r * Cos@Pi - f@r, 40, 10, 2, 40 ê 10.D ê 2D, r * Sin@Pi - f@r, 40, 10, 2, 40 ê 10.D ê 2D<,
8r, r1@40, 2, 40 ê 10.D + .001, r2@40, 2, 40 ê 10.D - .001<, PlotStyle Ø 8RGBColor@0, 0, 1D<D
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Ü Graphics Ü
Show@%29, %30, PlotRange Ø 88- 35, 35<, 8- 35, 35<<, AspectRatio Ø 1D
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30
-10
-20
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Ü Graphics Ü
r1@60, 3, 60 ê 20.D
r2@60, 3, 60 ê 20.D
31.7157
88.2843
Plot@k1@r, 60, 20, 3, 60 ê 20.D, 8r, r1@60, 3, 60 ê 20.D + .001, r2@60, 3, 60 ê 20.D - .001<D
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Hwrk3_13.nb
ParametricPlot@
8r * Cos@- f@r, 60, 20, 3, 60 ê 20.D ê 3D, r * Sin@- f@r, 60, 20, 3, 60 ê 20.D ê 3D<,
8r, r1@60, 3, 60 ê 20.D + .001, r2@60, 3, 60 ê 20.D - .001<, PlotStyle Ø 8RGBColor@1, 0, 0D<D
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Ü Graphics Ü
ParametricPlot@8r * Cos@2 Pi ê 3 - f@r, 60, 20, 3, 60 ê 20.D ê 3D,
r * Sin@2 Pi ê 3 - f@r, 60, 20, 3, 60 ê 20.D ê 3D<,
8r, r1@60, 3, 60 ê 20.D + .001, r2@60, 3, 60 ê 20.D - .001<, PlotStyle Ø 8RGBColor@0, 0, 1D<D
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ParametricPlot@8r * Cos@4 Pi ê 3 - f@r, 60, 20, 3, 60 ê 20.D ê 3D,
r * Sin@4 Pi ê 3 - f@r, 60, 20, 3, 60 ê 20.D ê 3D<,
8r, r1@60, 3, 60 ê 20.D + .001, r2@60, 3, 60 ê 20.D - .001<, PlotStyle Ø 8RGBColor@0, 1, 0D<D
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Hwrk3_13.nb
Show@%49, %50, %51, PlotRange Ø 88- 85, 85<, 8- 85, 85<<, AspectRatio Ø 1D
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Plot@k1@r, 100, 20, 5, 100 ê 20.D,
8r, r1@100, 5, 100 ê 20.D + .001, r2@100, 5, 100 ê 20.D - .001<D
0.35
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0.275
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ParametricPlot@
8r * Cos@- f@r, 100, 20, 5, 100 ê 20.D ê 5D, r * Sin@- f@r, 100, 20, 5, 100 ê 20.D ê 5D<,
8r, r1@100, 5, 100 ê 20.D + .001, r2@100, 5, 100 ê 20.D - .001<,
PlotStyle Ø 8RGBColor@1, 0, 0D<D
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Hwrk3_13.nb
ParametricPlot@8r * Cos@2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D,
r * Sin@2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D<,
8r, r1@100, 5, 100 ê 20.D + .001, r2@100, 5, 100 ê 20.D - .001<,
PlotStyle Ø 8RGBColor@0, 0, 1D<D
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ParametricPlot@8r * Cos@2 * 2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D,
r * Sin@2 * 2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D<,
8r, r1@100, 5, 100 ê 20.D + .001, r2@100, 5, 100 ê 20.D - .001<,
PlotStyle Ø 8RGBColor@0, 1, 0D<D
ParametricPlot@8r * Cos@3 * 2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D,
r * Sin@3 * 2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D<,
8r, r1@100, 5, 100 ê 20.D + .001, r2@100, 5, 100 ê 20.D - .001<,
PlotStyle Ø 8RGBColor@0, 1, 1D<D
ParametricPlot@8r * Cos@4 * 2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D,
r * Sin@4 * 2 Pi ê 5 - f@r, 100, 20, 5, 100 ê 20.D ê 5D<,
8r, r1@100, 5, 100 ê 20.D + .001, r2@100, 5, 100 ê 20.D - .001<,
PlotStyle Ø 8RGBColor@1, 0, 1D<D
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Ü Graphics Ü
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Ü Graphics Ü
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Show@%77, %78, %82, %83, %84, PlotRange Ø 88- 130, 130<, 8- 130, 130<<, AspectRatio Ø 1D
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