Related
I am using a quiver plot in MATLAB to simulate a velocity field. Now I would like the vectors produced by the quiver plot to be all the same length, so that they just indicate the vectors direction. The value of the velocity in each point should be illustrated by different colors then.
Is there a possibility to have quiver plotting vectors of same length?
That's my current code:
%defining parameters:
age = 900;
vis= 15;
turbulences = zeros(9,3);
a = 0.01;
spacing = 1000;
[x,y] = meshgrid(-100000:spacing:100000);%, 0:spacing:10000);
u = a;
v = 0;
n = 0;
for i = 1:4
turbulences(i,1) = -80000 + n;
turbulences(i,2) = 15000;
n = 15000 * i;
end
n = 0;
for i = 5:9
turbulences(i,1) = -15000 + n*5000;
turbulences(i,2) = 4000;
n = n+1;
end
for i = 1:4
turbulences(i,3) = -1000;
end
for i = 5:9
turbulences(i,3) = 800;
end
%compute velocities in x and y direction
for k = 1:9
xc = turbulences(k,1);
yc = turbulences(k,2);
r1 = ((x-xc).^2 + (y-yc).^2);
r2 = ((x-xc).^2 + (y+yc).^2);
u = u + turbulences(k,3)/2*pi * (((y-yc)./r1).*(1-exp(-(r1./(4*vis*age)))) - ((y+yc)./r2).*(1-exp(-(r2./(4*vis*age)))));
v = v - turbulences(k,3)/2*pi* (((x-xc)./r1).*(1-exp(-(r1./(4*vis*age)))) - ((x-xc)./r2).*(1-exp(-(r2./(4*vis*age)))));
end
quiver(x,y,u,v);
grid on;
Thank you for your help!
One way to do this would be to normalize each component of your vectors to +- 1 just to keep their direction.
un = u./abs(u); % normalized u
vn = v./abs(v); % normalized v
quiver(x, y, un, vn)
I want to create a relative axis in Matlab like the $\Delta I$-rulers in the following plot.
Before I start writing up a function that constructs it manually, I would like to know if there's way of creating an object with the NumericRuler-properties (like the default axes of a figure())
So I ended up using the link provided by Sardar Usama's comment as inspiration and wrote a function to create an axes-object relative to the values of a "parent"-axes:
function ax = create_value_axes(hAx, pos)
%% ax = create_value_axes(hAx, pos)
%
% Create axes at the value points of hAx.
%
% pos(1) = x-position
% pos(2) = y-position
% pos(3) = x-width
% pos(4) = y-width
%
% Get "parent" position and value limits
hAx_pos = hAx.Position;
hAx_xlm = hAx.XLim;
hAx_ylm = hAx.YLim;
% Get relative position increment pr value increment
x_step = hAx_pos(3) / (hAx_xlm(2) - hAx_xlm(1));
y_step = hAx_pos(4) / (hAx_ylm(2) - hAx_ylm(1));
% Set position
subaxes_abs_pos(1) = (pos(1)-hAx_xlm(1)) * x_step + hAx_pos(1);
subaxes_abs_pos(2) = (pos(2)-hAx_ylm(1)) * y_step + hAx_pos(2);
subaxes_abs_pos(3) = pos(3) * x_step;
subaxes_abs_pos(4) = pos(4) * y_step;
% Create axes
ax = axes('Position', subaxes_abs_pos);
% Remove background
ax.Color = 'none';
end
Sidenote: I found that I didn't need plotboxpos to get the correct positions of the "parent"-axes, using Matlab r2019b on macOS Mojave 10.14.6
Anyway, this is what I end up with:
Using the code:
% Just some random data
mockup_data_ild = [-10 -7 -4 0 4 7 10];
mockup_data_itd_45 = [-40 -20 -10 0 10 20 40];
mockup_data_itd_60 = [-30 -15 -5 0 5 15 30];
% Create figure
figure('Color', 'w')
x_axis_offset = [0 30];
hold on
% Plot 45 dB result
p1 = plot_markers(x_axis_offset(1) + mockup_data_ild, mockup_data_itd_45, ii);
% Plot 60 dB results
p2 = plot_markers(x_axis_offset(2) + mockup_data_ild, mockup_data_itd_60, ii);
p2.Color = p1.Color;
p2.HandleVisibility = 'off';
hold off
% Set axes properties
ax = gca;
ax.XAxis.TickValues = [x_axis_offset(1) x_axis_offset(2)];
ax.XAxis.TickLabels = {'45 dB' '60 dB'};
ax.XAxis.Limits = [x_axis_offset(1)-15 x_axis_offset(2)+15];
ax.XAxisLocation = 'top';
ax.YAxis.Limits = [-80 100];
ax.YAxis.Label.String = 'Interaural Time Difference, \Deltat, in samples';
ax.YGrid = 'on';
% Create 45 dB axis
ax2 = create_DeltaI_axis(ax, x_axis_offset(1));
% Create 60 dB axis
ax3 = create_DeltaI_axis(ax, x_axis_offset(2));
% Create legend
leg = legend(ax, {'P1'});
leg.Location = 'northwest';
%% Helpers
function ax = create_DeltaI_axis(hAx, x_pos)
y_pos = -70;
y_height = 170;
range = 20;
ax = create_value_axes(hAx, [x_pos-range/2 y_pos range y_height]);
ax.XAxis.TickValues = [0 .25 .5 .75 1];
ax.XAxis.TickLabels = {'-10'
'-5'
'0'
'5'
'10'};
ax.XAxis.Label.String = '\DeltaI';
ax.XGrid = 'on';
ax.XMinorGrid = 'on';
ax.YAxis.Visible = 'off';
end
function p = plot_markers(x, y, ii)
markers = {'square','^', 'v', 'o', 'd'};
p = plot(x, y);
p.LineWidth = 1.5;
p.LineStyle = 'none';
p.Marker = markers{ii};
end
Working on a little project to do with computer graphics. So far I have (I think) everything in order as the code below patches my world to the screen fine.
However, I have a final hurdle to jump: I would like the code to patch for different values of theta. In the code, it is set at 2*pi/4 but I would like to iterate and patch for every angle between 0:pi/4:2*pi. However, when I try to put the code in a for or while loop it doesn't seem to do what I expect, that is, to patch with one angle, then patch with another etc.
Really stuck I have tried a lot of stuff and now I'm just without any ideas. Would really appreciate any help or suggestions.
function world()
% Defining House Vertices
house_verts = [-5, 0, -5;
5, 0, -5;
5, 10, -5;
0,15,-5;
-5,10,-5;
-5,0,5;
5,0,5;
5,10,5;
0,15,5;
-5,10,5];
% Sorting out the homeogenous co-ordinates
ones = [1,1,1,1,1,1,1,1,1,1];
ones=transpose(ones);
house_verts = [house_verts, ones];
house_verts = transpose(house_verts);
% House faces
house_faces = [1,2,3,4,5;
2,7,8,3,3;
6,7,8,9,10;
1,6,10,5,5;
3,4,9,8,8;
4,5,10,9,9;
1,2,7,6,6];
world_pos = [];
% creating a street
street_vector = [1,0,1]; % the direction of the street
orthog_street_vector = [-1,0,1];
for i = 1:15
% current_pos1 and 2 will be the positions of the two houses
% opposite each other on the street
current_pos1 = 30*i*street_vector + 50*orthog_street_vector;
current_pos2 = 30*i*street_vector - 50*orthog_street_vector;
world_pos = [world_pos;current_pos1;current_pos2];
end
% initialising world vertices and faces
world_verts = [];
world_faces = [];
% Populating the street
for i =1:size(world_pos,1)
T = transmatrix(world_pos(i,:)); % a translation matrix
s = [1,1/2 + rand(),1];
S=scalmatrix(s); % a matrix for a random scaling of the height (y-coordinate)
Ry = rotymatrix(rand()*2*pi); % a matrix for a random rotation about the y-axis
A = T*Ry*S; % the compound transformation matrix to take the house into the world
obj_faces = size(world_verts,2) + house_faces; %increments the basic house faces to match the current object
obj_verts = A*house_verts;
world_verts = [world_verts, obj_verts]; % adds the vertices to the world
world_faces = [world_faces; obj_faces]; % adds the faces to the world
end
% initialising aligned vertices
align_verts = [];
% Aligning the vertices to the particular camera at angle theta
for elm = world_verts
x = 350 + 350*cos(2*pi/4);
z = 350 + 350*sin(2*pi/4);
y = 80;
u = [x,y,z];
v = [250,0,250];
d = v - u;
phiy = atan2(d(1),d(3));
phix = -atan2(d(2),sqrt(d(1)^2+d(3)^2));
T = transmatrix([-u(1),-u(2),-u(3)]);
Ry = rotymatrix(phiy);
Rx = rotxmatrix(phix);
A = Rx*Ry*T;
align_verts = [align_verts, A*elm];
end
% initialising projected vertices
proj_verts=[];
% Performing the projection
for elm = align_verts
proj = projmatrix(10);
projverts = proj*elm;
projverts = ((10/projverts(3))*projverts);
proj_verts = [proj_verts,projverts];
end
% Displaying the world
for i = 1:size(world_faces,1)
for j = 1:size(world_faces,2)
x(j) =proj_verts(1,world_faces(i,j));
z(j) = proj_verts(2,world_faces(i,j));
end
patch(x,z,'w')
end
end
function T = transmatrix(p)
T = [1 0 0 p(1) ; 0 1 0 p(2) ; 0 0 1 p(3) ; 0 0 0 1];
end
function S = scalmatrix(s)
S = [s(1) 0 0 0 ; 0 s(2) 0 0 ; 0 0 s(3) 0 ; 0 0 0 1];
end
function Ry = rotymatrix(theta)
Ry = [cos(theta), 0, -sin(theta),0;
0,1,0,0;
sin(theta),0,cos(theta),0;
0,0,0,1];
end
function Rx = rotxmatrix(phi)
Rx = [1, 0, 0, 0;
0, cos(phi), -sin(phi), 0;
0, sin(phi), cos(phi), 0;
0, 0, 0, 1];
end
function P = projmatrix(f)
P = [1,0,0,0
0,1,0,0
0,0,1,0
0,0,1/f,0];
end
Updated code: managed to get the loop to work but now there is some bug i don't understand when it does a full rotation again any help would be great.
function world()
% Defining House Vertices
house_verts = [-5, 0, -5;
5, 0, -5;
5, 10, -5;
0,15,-5;
-5,10,-5;
-5,0,5;
5,0,5;
5,10,5;
0,15,5;
-5,10,5];
% Sorting out the homeogenous co-ordinates
ones = [1,1,1,1,1,1,1,1,1,1];
ones=transpose(ones);
house_verts = [house_verts, ones];
house_verts = transpose(house_verts);
% House faces
house_faces = [1,2,3,4,5;
2,7,8,3,3;
6,7,8,9,10;
1,6,10,5,5;
3,4,9,8,8;
4,5,10,9,9;
1,2,7,6,6];
world_pos = [];
% creating a street
street_vector = [1,0,1]; % the direction of the street
orthog_street_vector = [-1,0,1];
for i = 1:15
% current_pos1 and 2 will be the positions of the two houses
% opposite each other on the street
current_pos1 = 30*i*street_vector + 50*orthog_street_vector;
current_pos2 = 30*i*street_vector - 50*orthog_street_vector;
world_pos = [world_pos;current_pos1;current_pos2];
end
% initialising world vertices and faces
world_verts = [];
world_faces = [];
% Populating the street
for i =1:size(world_pos,1)
T = transmatrix(world_pos(i,:)); % a translation matrix
s = [1,1/2 + rand(),1];
S=scalmatrix(s); % a matrix for a random scaling of the height (y-coordinate)
Ry = rotymatrix(rand()*2*pi); % a matrix for a random rotation about the y-axis
A = T*Ry*S; % the compound transformation matrix to take the house into the world
obj_faces = size(world_verts,2) + house_faces; %increments the basic house faces to match the current object
obj_verts = A*house_verts;
world_verts = [world_verts, obj_verts]; % adds the vertices to the world
world_faces = [world_faces; obj_faces]; % adds the faces to the world
end
% initialising aligned vertices
align_verts = [];
% initialising projected vertices
proj_verts=[];
% Aligning the vertices to the particular camera at angle theta
theta = 0;
t = 0;
while t < 100
proj_verts=[];
align_verts = [];
for elm = world_verts
x = 300 + 300*cos(theta);
z = 300 + 300*sin(theta);
y = 80;
u = [x,y,z];
v = [200,0,200];
d = v - u;
phiy = atan2(d(1),d(3));
phix = -atan2(d(2),sqrt(d(1)^2+d(3)^2));
T = transmatrix([-u(1),-u(2),-u(3)]);
Ry = rotymatrix(phiy);
Rx = rotxmatrix(phix);
A = Rx*Ry*T;
align_verts = [align_verts, A*elm];
end
% Performing the projection
for elm = align_verts
proj = projmatrix(6);
projverts = proj*elm;
projverts = ((6/projverts(3))*projverts);
proj_verts = [proj_verts,projverts];
end
% Displaying the world
for i = 1:size(world_faces,1)
for j = 1:size(world_faces,2)
x(j) = proj_verts(1,world_faces(i,j));
z(j) = proj_verts(2,world_faces(i,j));
end
patch(x,z,'w')
pbaspect([1,1,1]); % adjusts the aspect ratio of the figure
end
title('Projected Space', 'fontsize', 16, 'interpreter', 'latex')
xlabel('$x$', 'fontsize', 16, 'interpreter', 'latex')
ylabel('$z$', 'fontsize', 16, 'interpreter', 'latex')
zlabel('$y$', 'fontsize', 16, 'interpreter', 'latex')
axis([-5,5,-5,2,0,5]) % sets the axes limits
view(0,89)
pause(0.0000001)
theta = theta + 0.01;
clf
end
end
function T = transmatrix(p)
T = [1 0 0 p(1) ; 0 1 0 p(2) ; 0 0 1 p(3) ; 0 0 0 1];
end
function S = scalmatrix(s)
S = [s(1) 0 0 0 ; 0 s(2) 0 0 ; 0 0 s(3) 0 ; 0 0 0 1];
end
function Ry = rotymatrix(theta)
Ry = [cos(theta), 0, -sin(theta),0;
0,1,0,0;
sin(theta),0,cos(theta),0;
0,0,0,1];
end
function Rx = rotxmatrix(phi)
Rx = [1, 0, 0, 0;
0, cos(phi), -sin(phi), 0;
0, sin(phi), cos(phi), 0;
0, 0, 0, 1];
end
function P = projmatrix(f)
P = [1,0,0,0
0,1,0,0
0,0,1,0
0,0,1/f,0];
end
I want to move a red star marker along the spiral trajectory with an equal distance of 5 units between the red star points on its circumference like in the below image.
vertspacing = 10;
horzspacing = 10;
thetamax = 10*pi;
% Calculation of (x,y) - underlying archimedean spiral.
b = vertspacing/2/pi;
theta = 0:0.01:thetamax;
x = b*theta.*cos(theta)+50;
y = b*theta.*sin(theta)+50;
% Calculation of equidistant (xi,yi) points on spiral.
smax = 0.5*b*thetamax.*thetamax;
s = 0:horzspacing:smax;
thetai = sqrt(2*s/b);
xi = b*thetai.*cos(thetai);
yi = b*thetai.*sin(thetai);
plot(x,y,'b-');
hold on
I want to get a figure that looks like the following:
This is my code for the circle trajectory:
% Initialization steps.
format long g;
format compact;
fontSize = 20;
r1 = 50;
r2 = 35;
r3= 20;
xc = 50;
yc = 50;
% Since arclength = radius * (angle in radians),
% (angle in radians) = arclength / radius = 5 / radius.
deltaAngle1 = 5 / r1;
deltaAngle2 = 5 / r2;
deltaAngle3 = 5 / r3;
theta1 = 0 : deltaAngle1 : (2 * pi);
theta2 = 0 : deltaAngle2 : (2 * pi);
theta3 = 0 : deltaAngle3 : (2 * pi);
x1 = r1*cos(theta1) + xc;
y1 = r1*sin(theta1) + yc;
x2 = r2*cos(theta2) + xc;
y2 = r2*sin(theta2) + yc;
x3 = r3*cos(theta3) + xc;
y3 = r3*sin(theta3) + yc;
plot(x1,y1,'color',[1 0.5 0])
hold on
plot(x2,y2,'color',[1 0.5 0])
hold on
plot(x3,y3,'color',[1 0.5 0])
hold on
% Connecting Line:
plot([70 100], [50 50],'color',[1 0.5 0])
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0, 1, 1]);
drawnow;
axis square;
for i = 1 : length(theta1)
plot(x1(i),y1(i),'r*')
pause(0.1)
end
for i = 1 : length(theta2)
plot(x2(i),y2(i),'r*')
pause(0.1)
end
for i = 1 : length(theta3)
plot(x3(i),y3(i),'r*')
pause(0.1)
end
I can't think of a way to compute distance along a spiral, so I'm approximating it with circles, in hopes that it will still be useful.
My solution relies on the InterX function from FEX, to find the intersection of circles with the spiral. I am providing an animation so it is easier to understand.
The code (tested on R2017a):
function [x,y,xi,yi] = q44916610(doPlot)
%% Input handling:
if nargin < 1 || isempty(doPlot)
doPlot = false;
end
%% Initialization:
origin = [50,50];
vertspacing = 10;
thetamax = 5*(2*pi);
%% Calculation of (x,y) - underlying archimedean spiral.
b = vertspacing/(2*pi);
theta = 0:0.01:thetamax;
x = b*theta.*cos(theta) + origin(1);
y = b*theta.*sin(theta) + origin(2);
%% Calculation of equidistant (xi,yi) points on spiral.
DST = 5; cRes = 360;
numPts = ceil(vertspacing*thetamax); % Preallocation
[xi,yi] = deal(NaN(numPts,1));
if doPlot && isHG2() % Plots are only enabled if the MATLAB version is new enough.
figure(); plot(x,y,'b-'); hold on; axis equal; grid on; grid minor;
hAx = gca; hAx.XLim = [-5 105]; hAx.YLim = [-5 105];
hP = plot(xi,yi,'r*');
else
hP = struct('XData',xi,'YData',yi);
end
hP.XData(1) = origin(1); hP.YData(1) = origin(2);
for ind = 2:numPts
P = InterX([x;y], makeCircle([hP.XData(ind-1),hP.YData(ind-1)],DST/2,cRes));
[~,I] = max(abs(P(1,:)-origin(1)+1i*(P(2,:)-origin(2))));
if doPlot, pause(0.1); end
hP.XData(ind) = P(1,I); hP.YData(ind) = P(2,I);
if doPlot, pause(0.1); delete(hAx.Children(1)); end
end
xi = hP.XData(~isnan(hP.XData)); yi = hP.YData(~isnan(hP.YData));
%% Nested function(s):
function [XY] = makeCircle(cnt, R, nPts)
P = (cnt(1)+1i*cnt(2))+R*exp(linspace(0,1,nPts)*pi*2i);
if doPlot, plot(P,'Color',lines(1)); end
XY = [real(P); imag(P)];
end
end
%% Local function(s):
function tf = isHG2()
try
tf = ~verLessThan('MATLAB', '8.4');
catch
tf = false;
end
end
function P = InterX(L1,varargin)
% DOCUMENTATION REMOVED. For a full version go to:
% https://www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections
narginchk(1,2);
if nargin == 1
L2 = L1; hF = #lt; %...Avoid the inclusion of common points
else
L2 = varargin{1}; hF = #le;
end
%...Preliminary stuff
x1 = L1(1,:)'; x2 = L2(1,:);
y1 = L1(2,:)'; y2 = L2(2,:);
dx1 = diff(x1); dy1 = diff(y1);
dx2 = diff(x2); dy2 = diff(y2);
%...Determine 'signed distances'
S1 = dx1.*y1(1:end-1) - dy1.*x1(1:end-1);
S2 = dx2.*y2(1:end-1) - dy2.*x2(1:end-1);
C1 = feval(hF,D(bsxfun(#times,dx1,y2)-bsxfun(#times,dy1,x2),S1),0);
C2 = feval(hF,D((bsxfun(#times,y1,dx2)-bsxfun(#times,x1,dy2))',S2'),0)';
%...Obtain the segments where an intersection is expected
[i,j] = find(C1 & C2);
if isempty(i), P = zeros(2,0); return; end
%...Transpose and prepare for output
i=i'; dx2=dx2'; dy2=dy2'; S2 = S2';
L = dy2(j).*dx1(i) - dy1(i).*dx2(j);
i = i(L~=0); j=j(L~=0); L=L(L~=0); %...Avoid divisions by 0
%...Solve system of eqs to get the common points
P = unique([dx2(j).*S1(i) - dx1(i).*S2(j), ...
dy2(j).*S1(i) - dy1(i).*S2(j)]./[L L],'rows')';
function u = D(x,y)
u = bsxfun(#minus,x(:,1:end-1),y).*bsxfun(#minus,x(:,2:end),y);
end
end
Result:
Note that in the animation above, the diameter of the circle (and hence the distance between the red points) is 10 and not 5.
The below code is something that I am cooking up. I am plotting the orbits of the Sun, Mercury, Earth and the Moon. I have gotten this far into the project but the orbit of Mercury is terrifyingly wrong. This is seen by typing "SunEarthMoon(2,50)" at the command prompt and viewing the bottom left plot. The logic behind the project is utilizing Newton's Second Law toggled with the command "ode45" to find the positions of the bodies during a given time interval. I've been staring at this for far too long. Can anyone help to fix the orbit of Mercury?
function [] = SunEarthMoon(years,framerate)
%% Clean Up
close all
clc
%% Initializaion
x_earth = 147300000000; % [m]
x_mercury = 57.91e9; % [m]
v_earth = 30257; % [m/s]
v_mercury = 47362; % [m/s]
r_sat = 384748000; % earth surface [m]
r_earth = 6367000; % earth radius [m]
v_sat = 1023; % relative velocity from earth [m/s]
a = 5.145; % Angle to vertical (y) axis
b = 90; % Angle to horizontal (x) axis in xz plane
x_earth_o = [x_earth; 0; 0];
x_sun_o = [0; 0; 0];
x_mercury_o = [x_mercury; 0; 0];
x_sat_o = [x_earth+r_sat+r_earth; 0; 0];
v_earth_o = [0; v_earth; 0];
v_sun_o = [0; 0; 0];
v_mercury_o = [0; v_mercury; 0];
v_sat_o = v_sat*[cos(pi/180*b)*sin(pi/180*a); cos(pi/180*a); sin(pi/180*b)*sin(pi/180*a)] + v_earth_o;
interval = years*[0 31536000];
%% Error Control
h = [0.01 36000];
tol = 100000;
Options.AbsTol = tol;
Options.MaxStep = h(2);
Options.InitialStep = h(1);
%% Analysis
ao = [x_earth_o; v_earth_o; x_sun_o; v_sun_o; x_sat_o; v_sat_o; x_mercury_o; v_mercury_o];
[t, x] = ode45(#earthfinal,interval,ao,Options);
for i = 1:length(t)
R1(i) = (x(i,13)-x(i,1));
R2(i) = (x(i,14)-x(i,2));
R3(i) = (x(i,15)-x(i,3));
R(i) = sqrt(R1(i)^2+R2(i)^2+R3(i)^2);
end
T_index_earth = find([1; x(:,4)].*[x(:,4);1]<=0);
T_index_moon = find([1; R2(:)].*[R2(:); 1]<=0);
for i = 4:length(T_index_earth)
T_earth_semi(i-3) = (t(T_index_earth(i)-1)-t(T_index_earth(i-2)-1))/24/60/60;
end
T_earth = mean(T_earth_semi);
for i = 4:length(T_index_moon)
T_moon_semi(i-3) = (t(T_index_moon(i)-1)-t(T_index_moon(i-2)-1))/24/60/60;
end
T_moon = mean(T_moon_semi);
D_earth = 0;
for i = 2:(T_index_earth(4)-1)
D_earth = D_earth + sqrt((x(i,1)-x(i-1,1))^2+(x(i,2)-x(i-1,2))^2+(x(i,3)-x(i-1,3))^2);
end
D_moon = 0;
for i = 2:(T_index_moon(4)-1)
D_moon = D_moon + sqrt((R1(i)-R1(i-1))^2+(R2(i)-R2(i-1))^2+(R3(i)-R3(i-1))^2);
end
%% Plots
q = framerate;
scrsz = get(0,'ScreenSize');
figure('position', [0.05*scrsz(3) 0.05*scrsz(4) 0.75*scrsz(3) 0.85*scrsz(4)])
set(gcf,'name','Sun, Earth, and Moon Orbits')
for i = 1:length(t)/q
subplot(2,2,1)
plot3(x(1:i*q,1),x(1:i*q,2),x(1:i*q,3),'g',x(1:i*q,7),x(1:i*q,8),x(1:i*q,9),'r',x(1:i*q,13),x(1:i*q,14),x(1:i*q,15),'b',x(1:i*q,19),x(1:i*q,20),x(1:i*q,21),'black')
axis(1.1*[min(x(:,1)) max(x(:,1)) min(x(:,2)) max(x(:,2)) 2*min(x(:,15)) 2*max(x(:,15))])
xlabel('Universal X Coordinate (m)')
ylabel('Universal Y Coordinate (m)')
zlabel('Universal Z Coordinate (m)')
title('Relative Orbits')
legend('Earth','Sun','Moon')
hold on
plot3(x(i*q,1),x(i*q,2),x(i*q,3),'g-o',x(i*q,7),x(i*q,8),x(i*q,9),'r-o',x(i*q,13),x(i*q,14),x(i*q,15),'b-o',x(i*q,19),x(i*q,20),x(i*q,21),'black-o')
hold off
subplot(2,2,2)
plot3(R1(1:i*q),R2(1:i*q),R3(1:i*q),'b',zeros(1,i*q),zeros(1,i*q),zeros(1,i*q),'g')
axis(1.5*[min(R1) max(R1) min(R2) max(R2) min(R3) max(R3)])
xlabel('Universal X Coordinate (m)')
ylabel('Universal Y Coordinate (m)')
zlabel('Universal Z Coordinate (m)')
title('Relative Moon Orbit About Earth')
hold on
plot3(R1(i*q),R2(i*q),R3(i*q),'b-o',0,0,0,'g-o')
text(0,1.45*max(R2),1.40*max(R3),sprintf('Orbital Period, T = %3.5g days',T_moon))
text(0,1.45*max(R2),1.15*max(R3),sprintf('Orbital Circumference, D = %3.5g gigameters',D_moon*1e-9))
hold off
subplot(2,2,3)
plot(x(1:i*q,1),x(1:i*q,2),'g',x(1:i*q,7),x(1:i*q,8),'r', x(1:i*q,19),x(1:i*q,20),'black')
axis(1.5*[min(x(:,1)) max(x(:,1)) min(x(:,2)) max(x(:,2))])
xlabel('Universal X Coordinate (m)')
ylabel('Universal Y Coordinate (m)')
title('Relative Earth Orbit About Sun')
hold on
plot(x(i*q,1),x(i*q,2),'g-o',x(i*q,7),x(i*q,8),'r-o',x(i*q,19),x(i*q,20),'black-o')
text(1.45*min(x(:,1)),1.40*max(x(:,2)),sprintf('Orbital Period, T = %3.5g days',T_earth))
text(1.45*min(x(:,1)),1.25*max(x(:,2)),sprintf('Orbital Circumference, D = %3.5g gigameters',D_earth*1e-9))
text(1.45*min(x(:,1)),1.40*min(x(:,2)),sprintf('Time, t = %3.3g days',round(t(q*i)/24/60/60)))
hold off
subplot(2,2,4)
plot(t(1:i*q)/(60*60*24),R(1:i*q)/1000,'b')
axis([t(1)/24/60/60 t(end)/24/60/60 0.999*min(R)/1000 1.001*max(R)/1000])
xlabel('Time,t (days)')
ylabel('Orbit Radius, R (km)')
title('Moon-Earth Distance')
hold on
plot(t(i*q)/(60*60*24),R(i*q)/1000,'b-o')
hold off
drawnow
end
end
%% Differential Equation Function
function [udot]= earthfinal(t,u)
m_earth = 5.9742e24; % [kg]
m_mercury = 3.285e23; % [kg]
m_sun = 1.98892e30; % [kg]
m_sat = 11110; % [kg]
G = 6.67300e-11; %[(m)^3(kg)^-1(s)^-2];
d_earth_sun = sqrt((u( 7,1)-u(1,1))^2+(u( 8,1)-u(2,1))^2+(u( 9,1)-u(3,1))^2);
d_earth_sat = sqrt((u(13,1)-u(1,1))^2+(u(14,1)-u(2,1))^2+(u(15,1)-u(3,1))^2);
d_sun_sat = sqrt((u(13,1)-u(7,1))^2+(u(14,1)-u(8,1))^2+(u(15,1)-u(9,1))^2);
d_mercury_sun = sqrt((u(7,1) -u(19,1))^2 + (u(8,1) - u(20,1))^2 + (u(9,1)-u(21,1))^2);
d_mercury_earth = sqrt((u(1,1) -u(19,1))^2 + (u(2,1) - u(20,1))^2 + (u(3,1)-u(21,1))^2);
d_mercury_sat = sqrt((u(13,1) -u(19,1))^2 + (u(14,1) - u(20,1))^2 + (u(15,1)-u(21,1))^2);
% Earth motion
udot( 1,1) = u(4,1);
udot( 2,1) = u(5,1);
udot( 3,1) = u(6,1);
udot( 4,1) = m_sun*G*(u(7,1)-u(1,1))/d_earth_sun^3 + m_sat*G*(u(13,1)-u(1,1))/d_earth_sat^3 + m_mercury*G*(u(19,1)-u(1,1))/d_mercury_earth^3;
udot( 5,1) = m_sun*G*(u(8,1)-u(2,1))/d_earth_sun^3 + m_sat*G*(u(14,1)-u(2,1))/d_earth_sat^3 + m_mercury*G*(u(20,1)-u(2,1))/d_mercury_earth^3;
udot( 6,1) = m_sun*G*(u(9,1)-u(3,1))/d_earth_sun^3 + m_sat*G*(u(15,1)-u(3,1))/d_earth_sat^3 + m_mercury*G*(u(21,1)-u(3,1))/d_mercury_earth^3;
% Sun Motion
udot( 7,1) = u(10,1);
udot( 8,1) = u(11,1);
udot( 9,1) = u(12,1);
udot(10,1) = m_earth*G*(u(1,1)-u(7,1))/d_earth_sun^3 + m_sat*G*(u(13,1)-u(7,1))/d_sun_sat^3 + m_mercury*G*(u(19,1)-u(7,1))/d_mercury_sun^3;
udot(11,1) = m_earth*G*(u(2,1)-u(8,1))/d_earth_sun^3 + m_sat*G*(u(14,1)-u(8,1))/d_sun_sat^3 + m_mercury*G*(u(20,1)-u(8,1))/d_mercury_sun^3;
udot(12,1) = m_earth*G*(u(3,1)-u(9,1))/d_earth_sun^3 + m_sat*G*(u(15,1)-u(9,1))/d_sun_sat^3 + m_mercury*G*(u(21,1)-u(9,1))/d_mercury_sun^3;
% Satellite Motion
udot(13,1) = u(16,1);
udot(14,1) = u(17,1);
udot(15,1) = u(18,1);
udot(16,1) = m_earth*G*(u(1,1)-u(13,1))/d_earth_sat^3 + m_sun*G*(u(7,1)-u(13,1))/d_sun_sat^3 + m_mercury*G*(u(19,1)-u(13,1))/d_mercury_sat^3;
udot(17,1) = m_earth*G*(u(2,1)-u(14,1))/d_earth_sat^3 + m_sun*G*(u(8,1)-u(14,1))/d_sun_sat^3 + m_mercury*G*(u(20,1)-u(14,1))/d_mercury_sat^3;
udot(18,1) = m_earth*G*(u(3,1)-u(15,1))/d_earth_sat^3 + m_sun*G*(u(9,1)-u(15,1))/d_sun_sat^3 + m_mercury*G*(u(21,1)-u(15,1))/d_mercury_sat^3;
% Mercury Motion
udot(19,1) = u(22,1);
udot(20,1) = u(23,1);
udot(21,1) = u(24,1);
udot(22,1) = m_sun*G*(u(7,1)-u(19,1))/d_mercury_sun^3 + m_earth*G*(u(1,1)-u(19,1))/d_mercury_earth^3 + m_sat*G*(u(13,1)-u(19,1))/d_mercury_sat^3;
udot(23,1) = m_sun*G*(u(8,1)-u(20,1))/d_mercury_sun^3 + m_earth*G*(u(2,1)-u(20,1))/d_mercury_earth^3 + m_sat*G*(u(14,1)-u(20,1))/d_mercury_sat^3;
udot(24,1) = m_sun*G*(u(9,1)-u(21,1))/d_mercury_sun^3 + m_earth*G*(u(3,1)-u(21,1))/d_mercury_earth^3 + m_sat*G*(u(15,1)-u(21,1))/d_mercury_sat^3;
end