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I need help with programming in MATLAB. The following code transforms cartesian coordinates to the kepler elements. Can you give me the code for transforming kepler orbital elements to cartesian coordinates. The following code gives the 6 kepler elements. Transform those elements into cartesian coordinate that match the values under the Example Usage part of the code.
% Example usage:
x = 1000;
y = 2000;
z = 3000;
vx = 4;
vy = -3;
vz = 2;
[a, ecc, inc, raan, argp, f] = cart2orb(x, y, z, vx, vy, vz);
% Display the results
disp(['Semi-Major Axis (a): ', num2str(a), ' km']);
disp(['Eccentricity (ecc): ', num2str(ecc)]);
disp(['Inclination (inc): ', num2str(inc), ' degrees']);
disp(['Right Ascension of Ascending Node (raan): ', num2str(raan), ' degrees']);
disp(['Argument of Perigee (argp): ', num2str(argp), ' degrees']);
disp(['True Anomaly (f): ', num2str(f), ' degrees']);
function [a, e, inc, raan, argp, f] = cart2orb(x, y, z, vx, vy, vz)
% Gravitational constant for Earth (μ⊕)
mu = 398600.4418; % km^3/s^2
% Calculate position and velocity
r = [x; y; z]; % Position vector
v = [vx; vy; vz]; % Velocity vector
% Calculate orbital parameters
h = cross(r, v); % Specific angular momentum vector
n = cross([0; 0; 1], h); % Nodal vector
% Eccentricity (ecc)
e_vec = (cross(v,h)/mu) - (r/norm(r));
%e_vec = ((norm(v)^2 - mu/norm(r)) * r - dot(r, v) * v) / mu;
e = norm(e_vec);
% Semi-major axis (a)
a = (dot(h,h)/mu) / (1-e^2);
%a = 1 / (2/norm(r) - norm(v)^2/mu_earth);
% Inclination (inc)
inc = acosd(h(3) / norm(h));
% Right Ascension of Ascending Node (raan)
raan = atan2d(n(2), n(1));
raan = mod(raan + 360, 360); % Ensure raan is in the range [0, 360)
% Argument of Perigee (argp)
argp = atan2d(dot(n, cross(e_vec, h)), dot(n, e_vec));
argp = mod(argp + 360, 360); % Ensure argp is in the range [0, 360)
% True Anomaly (f)
f = atan2d(dot(e_vec, cross(h, r)), dot(e_vec, r));
f = mod(f + 360, 360); % Ensure f is in the range [0, 360)
end
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