Mathematica Asked on March 19, 2021
Please I would like to plot, in the same graph, these two curves. How can I do that?
Manipulate[
ListPlot[Table[
NIntegrate[
Sqrt[((2*(Exp[(r)/(2)] - ((v0)^2)) ))/(r*
Exp[(r)/(2)] - ((2*(Exp[(r)/(2)] - ((v0)^2)) )))], {r,
(2*(1)*(1 + (
LambertW[((( 0^2 ) - (v0^2))/(Exp[
1]))] ))), (2*(1)*(1 + (
LambertW[((( u^2 ) - (v0^2))/(Exp[1]))] )))}], {u, 0, k,
1}], Joined -> True, InterpolationOrder -> 1], {k, 1,
20}, {v0, -0.9, 0.9}]
and
Manipulate[
ListPlot[Table[
NIntegrate[-Sqrt[((2*(Exp[(r)/(2)] - ((v0)^2)) ))/(r*
Exp[(r)/(2)] - ((2*(Exp[(r)/(2)] - ((v0)^2)) )))], {r,
(2*(1)*(1 + (
LambertW[((( 0^2 ) - (v0^2))/(Exp[
1]))] ))), (2*(1)*(1 + (
LambertW[((( u^2 ) - (v0^2))/(Exp[1]))] )))}], {u, 0, k,
1}], Joined -> True, InterpolationOrder -> 1], {k, 1,
20}, {v0, -0.9, 0.9}]
I think you're asking for the following:
Manipulate[
ListPlot[{Table[NIntegrate[Sqrt[((2*(Exp[(r)/(2)] - ((v0)^2))))/
(r*Exp[(r)/(2)] - ((2*(Exp[(r)/(2)] - ((v0)^2)))))],
{r, (2*(1)*(1 + (LambertW[(((0^2) - (v0^2))/(Exp[1]))]))),
(2*(1)*(1 + (LambertW[(((u^2) - (v0^2))/(Exp[1]))])))}], {u, 0, k, 1}],
Table[NIntegrate[-Sqrt[((2*(Exp[(r)/(2)] - ((v0)^2))))/
(r*Exp[(r)/(2)] - ((2*(Exp[(r)/(2)] - ((v0)^2)))))],
{r, (2*(1)*(1 + (LambertW[(((0^2) - (v0^2))/(Exp[1]))]))),
(2*(1)*(1 + (LambertW[(((u^2) - (v0^2))/(Exp[1]))])))}], {u, 0, k, 1}]},
Joined -> True, InterpolationOrder -> 1],
{{k, 5}, 1, 20},
{v0, -0.9, 0.9}
]
Correct answer by JimB on March 19, 2021
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