| Author |
Comment/Response |
Ryan
|
 09/01/10 10:33am
I am not sure why I am having troubles with this. The code is below. The math is correct, but it gives me an empty plot. Any ideas where I went wrong? I attached the notebook.
Thanks
\[Phi][\[Beta]_][u_, v_] :=
4 ArcTan[Exp[(\[Beta]/\[Rho]) u + v (1/(\[Rho]*\[Beta]))]];
xx := Exp[(\[Beta]/\[Rho])*u + v (1/(\[Rho]*\[Beta]))];
D[\[Phi][\[Beta]][u, v], u, v];
Simplify[D[\[Phi][\[Beta]][u, v], u, v]]
LHS := 4 (1/
Sqrt[xx^2 + 1]) (xx/(Sqrt[xx^2 + 1])) (2 (1/Sqrt[xx^2 + 1])^2 - 1)
Simplify[LHS]
\[Zeta][\[Beta]_] := 2 ArcTan[\[Beta]]
\[Zeta]1 := \[Zeta][1]
\[Zeta]2 := \[Zeta][4]
\[Chi][\[Lambda]_][u_, v_] := (
u (1 - Cos[\[Lambda]]) + v (1 + Cos[\[Lambda]]))/(\[Rho]*
Sin[\[Lambda]]);
\[Theta][\[Psi]_] := 2 ArcTan[Exp[\[Psi]]];
\[CapitalTheta][\[Zeta]11_, \[Zeta]12_, \[Chi]11_, \[Chi]12_] :=
2 ArcTan[(
Sin[(\[Zeta]11 + \[Zeta]12)/2] Sinh[(\[Chi]11 - \[Chi]12)/2])/(
Sin[(\[Zeta]12 - \[Zeta]11)/2] Cosh[(\[Chi]11 + \[Chi]12)/2])];
\[Chi]One := \[Chi][\[Zeta]1][u, v];
\[Chi]Two := \[Chi][\[Zeta]2][u, v];
\[Theta]One := \[Theta][\[Chi]One];
\[Theta]Two := \[Theta][\[Chi]Two];
\[CapitalTheta]One := \[CapitalTheta][\[Zeta]1, \[Zeta]2, \[Chi]One, \
\[Chi]Two];
\[Phi]prime[\[Beta]_] := \[Phi][\[Beta]][u, v] + \[Rho]*
Sin[\[Zeta]2][
Cos[\[CapitalTheta]One]/
Cos[\[Theta]One] D[\[Phi][\[Beta]][u, v], u] -
Sin[\[CapitalTheta]One]/
Sin[\[Theta]One] D[\[Phi][\[Beta]][u, v], v]];
func[u, v] = \[Phi]prime[1][u, v] /. \[Rho] -> 1
Plot3D[func[u, v], {u, 0, 333}, {v, .01, 444}]
Attachment: Tractrix.nb, URL: , |
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