# Plot a complex function as a vector along a curve

I have y a function of x and a parameter k. I use but don't really understand

Plot[Evaluate@Table[y[x,k],{k,{.01,.02,3,4,6}}],{x,.171,300},PlotRange etc.


to plot (stability) k contours in x,y space. Sometimes my contours of different k can cross.

Then I have a complex (mode) function c(x,y,k) magnitude m polar angle a of y,x, and k and periodically along each contour would like to plot this function, for instance as a small vector of length log m and polar angle a?

Is there a way this or something like it can be done in Mathematica? Thank you for reading this and thinking about it.

P.S.2 Now I am thinking to superimpose with Show my existing contourplot with vectorfieldplots of c for eack k with all regions excluded except aceptably close to the contour. Don't know if this will have to be done by hand for each k, or can be automated? Haven't worked out the coding

P.S.1 I have spared you the horror of y[x,k] which is many lines long involving the Theodorsen function which is a rational function of modified Bessel functions of the second kind of imaginary argument because it is besides the point.

• Sample functions for y and c would be useful. They don't have to be your actual complicated functions. Sep 15, 2017 at 16:29

Something like this?

f[x_, y_, k_] := Sin[x + k] - y

ContourPlot[f[x, y, #] & /@ {1, 3, 5} == 0, {x, -5, 5}, {y, -5, 5}]

• This does the first part, but it more indirectable and numerical when FF is invertible into y= . In any case it doesn'solve the second question of how to plot an imgainary function along eachof these contours.FF[x : _, y : _, k : _] = Sin[x + k] - y; ContourPlot[FF[x, y, #] & /@ {1, 3, 5} == 0, {x, -5, 5}, {y, -5, 5}] Sep 15, 2017 at 14:42
ListVectorPlot[
Table[{{x, Sin[x]}, {2 x, x*x}}, {x, -1.57, 1.57, .1}]
, VectorPoints -> All
]


sort of thing I wanted. VectorPoints switch is vital. vx=2x vy=x*x along y=sin x