MATLAB: How to realize ‘contour’ plotting with different spacings

contourdifferent spacingsMATLABtoo dense

I want to visualize the potential field of the Earth-Moon system. When I used the contour command, the contour lines which close to the Earth is too dense (see fig.1)

contour( x_EM2 , y_EM2 , V_matrix' , 100 )

If I reduce the quantity of the isolines, the isolines which close to the Moon will vanish (see fig.2).

contour( x_EM2 , y_EM2 , V_matrix' , 20 )

How to realize 'contour' plotting with different spacings or any idea of reducing the isolines close to the Earth without any lost of isolines close to the Moon?

Best Wishes

Best Answer

Instead of calling the function with 100 to get 100 iso-spaced contourlines you should calculate the potential-levels of interest and give that array:

C_levels = C0./linspace(r0,rmax,100); % where C0 R0 and rmax are for you to choose
contour( x_EM2 , y_EM2 , V_matrix' , C_levels )

HTH

Related Solutions

MATLAB: How to sepearte these two spehrical Objects – Earth and Moon – to get one Moon and one Earth? So far I get two Moon’s or either two Earth

Hi,

When you are executing the below line, It is returning both the Earth's surface plot and Moon's surface plot. So you are editing both surface plots when you edit the object h.

h = findobj('Type','surface');
set(h,'CData',moon,'FaceColor','texturemap','edgecolor','none')

Instead of using find function, you can directly store the output of surf function as h2 and h variables in this case.

h2 = surf(X,Y,Z)
h = surf(X2+15,Y2-15,-Z2)

Hope this helps.

MATLAB: Problems with simulation of Earth-Moon trajectories around the Sun

I haven't looked at your derivative equations yet, but the order is definitely wrong. E.g., take the first two elements:

ic=[r0(1,1);r0(1,2);v0(1,1);v0(1,2);... %initial conditions for Earth
    r0(2,1);r0(2,2);v0(2,1);v0(2,2)]; %initial conditions for Moon

Clearly, the first two elements of your state vector are the position elements for the Earth. But then in your derivative function:

f=@(t,x) [x(3);-G*(m(1)*x(1)/(x(1)^2+x(2)^2)^(3/2)+m(3)*(x(1)-x(5))/((x(1)-x(5))^2+(x(2)-x(6))^2)^(3/2));... %equation for Earth (x)
        x(4);-G*(m(1)*x(2)/(x(1)^2+x(2)^2)^(3/2)+m(3)*(x(2)-x(6))/((x(1)-x(5))^2+(x(2)-x(6))^2)^(3/2));... %equation for Earth (y)
        x(7);-G*(m(1)*x(5)/(x(5)^2+x(6)^2)^(3/2)+m(2)*(x(5)-x(1))/((x(5)-x(1))^2+(x(6)-x(2))^2)^(3/2));... %equation for Moon (x)
        x(8);-G*(m(1)*x(6)/(x(5)^2+x(6)^2)^(3/2)+m(2)*(x(6)-x(2))/((x(5)-x(1))^2+(x(6)-x(2))^2)^(3/2))]; %equation for Moon (y)

in that 2nd spot you have the velocity derivative, not the position derivative. This does not match your state vector ic. So at the very least, change the order of your derivative. E.g.,

f=@(t,x) [x(3);...
           x(4);...
          -G*(m(1)*x(1)/(x(1)^2+x(2)^2)^(3/2)+m(3)*(x(1)-x(5))/((x(1)-x(5))^2+(x(2)-x(6))^2)^(3/2));... %equation for Earth (x)
          -G*(m(1)*x(2)/(x(1)^2+x(2)^2)^(3/2)+m(3)*(x(2)-x(6))/((x(1)-x(5))^2+(x(2)-x(6))^2)^(3/2));... %equation for Earth (y)
         x(7);...
         x(8);...
        -G*(m(1)*x(5)/(x(5)^2+x(6)^2)^(3/2)+m(2)*(x(5)-x(1))/((x(5)-x(1))^2+(x(6)-x(2))^2)^(3/2));... %equation for Moon (x)
        -G*(m(1)*x(6)/(x(5)^2+x(6)^2)^(3/2)+m(2)*(x(6)-x(2))/((x(5)-x(1))^2+(x(6)-x(2))^2)^(3/2))]; %equation for Moon (y)

And then as a side comment I would suggest you double check your initial conditions for the moon velocity. Seems to me that it should be close to the earth velocity but that is not the case in your ic vector.

Best Answer

Related Solutions

MATLAB: How to sepearte these two spehrical Objects – Earth and Moon – to get one Moon and one Earth? So far I get two Moon’s or either two Earth

MATLAB: Problems with simulation of Earth-Moon trajectories around the Sun

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