Alkuviikko 8, demo 127

Input := 


f={(4-u Sin[v])Cos[2v], (4-u Sin[v])Sin[2v], u Cos[v]}

Output =

{Cos[2 v] (4 - u Sin[v]), (4 - u Sin[v]) Sin[2 v], u Cos[v]}

Input := 

ParametricPlot3D[f,{u,-1,1},{v,0,Pi},PlotPoints->{2,36}]

Output =

-Graphics3D-

Input := 

<<LinearAlgebra`CrossProduct`

Input := 

n=Simplify[Cross[D[f,u],D[f,v]]]

Output =

{Cos[v] (-8 Cos[2 v] + u Sin[v] + u Sin[3 v]), 
 
  u                u Cos[4 v]
  - - u Cos[2 v] - ---------- - 4 Sin[v] - 4 Sin[3 v], 
  2                    2
 
  2 Sin[v] (-4 + u Sin[v])}

Input := 

{nx,ny,nz}=n;

Input := 

kulma=ArcTan[ nz/Sqrt[nx^2+ny^2] ]

Output =

ArcTan[(2 Sin[v] (-4 + u Sin[v])) / 
 
         u                u Cos[4 v]
   Sqrt[(- - u Cos[2 v] - ---------- - 4 Sin[v] - 4 Sin[3 v])
         2                    2
 
      2         2                                      2
        + Cos[v]  (-8 Cos[2 v] + u Sin[v] + u Sin[3 v]) ]]

Input := 

Plot[kulma /. u->1, {v,0,Pi}];

Input := 

<<Graphics`PlotField3D`

Input := 

ListPlotVectorField3D[Table[{f,n},{v,0,Pi,Pi/32}] /. u->1,
ScaleFunction->(0.9&),VectorHeads->True];

Input := 

Plot[kulma /. u->1, {v,0,2Pi}];

Input := 

ListPlotVectorField3D[Table[{f,n},{v,0,2Pi,Pi/40}] /. u->1,
ScaleFunction->(0.9&),VectorHeads->True];