# How to combine a ContourPlot with a Manipulate[Parametric Plot]

I have this code of an orbit at a Lagrange Point of the Sun-Jupiter system

Alpha = 0.000953875;
r01[x_, y_] := Sqrt[(x - Alpha)^2 + y^2];
r02[x_, y_] := Sqrt[(x + 1 - Alpha)^2 + y^2];
x00 = -0.509;
y00 = 0.883;
u00 = 0.0259;
v00 = 0.0149;
tmax = 600;

solution = NDSolve[{x'[t] == u[t], y'[t] == v[t],
u'[t] == (-(1 - Alpha) (x[t] - Alpha))/r01[x[t], y[t]]^3 - (
Alpha (x[t] + 1 - Alpha))/r02[x[t], y[t]]^3 + x[t] + 2 v[t],

v'[t] == -(((1 - Alpha) y[t])/r01[x[t], y[t]]^3 ) - (Alpha y[t])/
r02[x[t], y[t]]^3 + y[t] - 2 u[t],

x == x00, y == y00,
u == u00, v == v00}, {x, y, u, v}, {t, 0, tmax}];


and i can manipulate said result with this code

Manipulate[ParametricPlot[Evaluate[{x[t], y[t]} /. solution], {t, 0, b},
PlotRange -> {{-0.9, -0.1}, {0.4, 1}}], {b, 0.01, 150}] I also have a contour plot

plot1 = ContourPlot[-((1 - a)/Sqrt[(x - a)^2 + y^2]) - a/
Sqrt[(x + 1 - a)^2 + y^2] - 1/2 (x^2 + y^2), {x, -1.65,
1.65}, {y, -1.65, 1.65}, AxesLabel -> {x, y}] Using the Show command, i cant manage to put them together, it says "Could not combine the graphics objects in Show", how can i combine them?

## 1 Answer

It looks like you may have tried to combine ContourPlot with Manipulate. This will not work because Show cannot combine a Graphics object with a Manipulate object. Instead have Show inside Manipulate itself.

Manipulate[
Show[plot1,
ParametricPlot[Evaluate[{x[t], y[t]} /. solution], {t, 0, b},
PlotRange -> {{-0.9, -0.1}, {0.4, 1}}]], {b, 0.01, 150}]


BTW your code for ContourPlot does not have the value for a. I took a to be 1 just to check.

• YES! Thank you so much! You're right, i forgot the value of a ,it was 0.001. Say, you helped me to show one orbit in that ContourPlot, i have other 4 solutions that cover other 4 areas of said ContourPlot, named "solution1, solution2, etc,.." How do i plot them altogether each, with its manipulate, in the ContourPlot? Should i make a list of 4 ParametricPlots? – Hector Manuel Chacon Carrillo Sep 25 '18 at 2:11
• It seems like you can solve the equations to get all 4 solutions and plot them all together using one ParametricPlot. and Use ContourPlot to show the contours. Manipuate can be wrapped Show as before. – Lotus Sep 25 '18 at 2:16