How draw an ellipse by acquiring points in 3D

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Morteza.Moslehi
Morteza.Moslehi 2016-12-16
评论： Madeleine Foster 2018-3-11
Hi. I have solved an Orbital Mechanics question about orbiting and acquired three points about the orbits, for example R1=(-9.5i 6.04j 3.1k)*10^3 and R2=(-9.6i 6.03j 3.4k)*10^3 as you see, the orbits are ellipse. i want to show it in cartesian axis. how can i do this..? should i use plot3 formation ? would you please help me please?
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Adam
Adam 2016-12-16
@Taha Smith. Please reply with comments rather than flagging someone's comment. Flags are used for reporting spam or other inappropriate content.

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Morteza.Moslehi
Morteza.Moslehi 2016-12-22
编辑：KSSV 2016-12-22
answer is: step 1:
function [r,v] = coes_RV(h,inc,RA,e,omega,theta)
%From the orital elements, the position and velocity vectors are is found.
%The Inputs are inputed the following matter:
% h is angular momentum in km^2/s
% inc is inclination in radians
% RA is right ascension of ascending node in radians
% e is eccelntricity (unitless)
% omega is argument of perigee in radians
% theta is true anomaly in radians
%Equations (EQN) used come from Curtis
mu = 398600; %Gravitational parameter of Earth (km^3/s^2)
%Now following Algorithm 4.2 from Curtis, I use EQN. 4.37 to find r in
%perifocal frame, and EQN 4.38 to find v in perifocal plane
rperi = h^2/mu/(1+e*cos(theta))*[cos(theta); sin(theta); 0]; % (km)
vperi = mu/h.*[-sin(theta); e + cos(theta); 0]; % (km/s)
%Next use EQN 4.44 to find transformation matrix from perifocl to
%geocentric equatorial coordinates
Qperi=[cos(RA)*cos(inc)*sin(omega)+cos(RA)*cos(omega) -sin(RA)*cos(inc)*cos(omega)-cos(RA)*sin(omega) sin(RA)*sin(inc);
cos(RA)*cos(inc)*sin(omega)+sin(RA)*cos(omega) cos(RA)*cos(inc)*cos(omega)-sin(RA)*sin(omega) -cos(RA)*sin(inc);
sin(inc)*sin(omega) sin(inc)*cos(omega) cos(inc)];
%Finally use, EQN 4.46 to find the r and V in the geocentric equatorial
%plane
r=Qperi*rperi; %in km
v=Qperi*vperi; %in km/s
%Convert r and v into row vectors
r = r'; %km
v = v'; %km/s
step 2:
function [accel] = orbit(t,y)
%y is the initial conditions, and time is in seconds
%Set constant values
mu = 398600; %Gravitational parameter of Earth (km^3/s^2)
%Pull out the initial conditions to components
rx=y(1); %km
ry=y(2); %km
rz=y(3); %km
vx=y(4); %km/s
vy=y(5); %km/s
vz=y(6); %km/s
%Normalize the position vector for futre use
R=norm([rx, ry, rz]); %Find acceleration from the position vector
ax=-mu*rx/R^3; %km/s^2
ay=-mu*ry/R^3; %km/s^2
az=-mu*rz/R^3; %km/s^2
%Set up new conditions after t seconds
accel = [vx; vy; vz; ax; ay; az];
step 3:
%Senior Project
close all
clear all
clc
%First state initial orbital elements in order to find initial r and v in
%geocentric equatorial coordinates
%Set constants
Re = 6378; %Radius of Earth (km)
mu = 398600; %Gravitational Parameter of Earth (km^3/s^2)
%Angular Momentum
h0 = 133929.0857; %km^2/s
%Inclination
inc0 = 45*pi/180; %radians
%Right Ascension of Ascending Node
RA0 = 0; %radians
%Eccentricity
e0 = 0;
%Argument of Perigee
omega0 = 0*pi/180; %radians
%True Anomaly
theta0 = 30*pi/180; %radians
%Now find r in km and v in km/s
[r0,v0] = coes_RV(h0,inc0,RA0,e0,omega0,theta0);
%Find Range
range0 = norm(r0) - Re; %in km
%Find Period of orbit
T0 = 2*pi/sqrt(mu)*(norm(r0))^(1.5); %in seconds
%Now these are the initial conditions and time span
y0 = [r0 v0]; t0 = [0 172800]; %in seconds
% t0 = [0 T0]; %in seconds
%Use ode45 to get orbit
[t,y] = ode45('orbit', t0, y0);
% %Plot Orbit
% plot3(y(:,1), y(:,2), y(:,3))
% %Simulation
% for i = 1:length(t)
% comet3(y(1:i,1), y(1:i,2), y(1:i,3))
% drawnow
% end
%Simulation
for i = 1:length(t)
plot3(y(1:i,1), y(1:i,2), y(1:i,3))
drawnow
end
give thanks to Nancy Teresa Cabrera too.

更多回答（1 个）

José-Luis
José-Luis 2016-12-16
Adapt to your needs:
z = [0.5,1];
fx = @(x) sin(x);
fy = @(x) cos(x);
t = linspace(0,2*pi,101);
plot3(fx(t),fy(t),repmat(z(1),1,numel(t)));
hold on
plot3(fx(t),fy(t),repmat(z(2),1,numel(t)));
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Morteza.Moslehi
Morteza.Moslehi 2016-12-22
@José-Luis thanks for your favor there. i found it
Morteza.Moslehi
Morteza.Moslehi 2017-2-23
in following this solution, i want to change parameters of radius in Cartesian coordinate to spherical coordinate. i know i should use this code:
[teta,phi,r] = cart2sph (x,y,z)
right? how can I plot " teta,phi,r" in spherical coordinate? would you please help me?
i want to demonstrate a spherical and show this orbit on that.
regards

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