轨道力学基本子程序包括位置速度和轨道根数

% Richard Rieber % September 26, 2006 % rrieber@gmail.com % % function [a,ecc,inc,Omega,w,nu,w_true,u_true,lambda_true] = elorb(R,V) % % function [a,ecc,inc,Omega,w,nu] = elorb(R,V,U) % % function [...] = elorb(R,V,U,tol) % % Purpose: This function converts ECI Cartesian coordinates (R & V) % to Kepler orbital elements (a, e, i, O, w, nu). % This function is derived from algorithm 9 on pg. 120 of % David A. Vallado's Fundamentals of Astrodynamics and % Applications (2nd Edition) % % Inputs: R: n x 3 radius vector from the center of the Earth to the % spacecraft (ECI coordinates) in km. n rows should be used % for multiple inputs % V: A n x 3 velocity vector of the space craft in km/s. % n rows should be used for multiple inputs % U: Gravitational constant of body being orbited (km^3/s^2). Default is Earth % at 398600.4415 km^3/s^2. [OPTIONAL] % tol: A tolerance value for checking equality. Default is 10^-8. % [OPTIONAL] % % Outputs: The user has two options for outputs. If 6 outputs are asked for, the % normal 6 Kepler elements will be returned (a,ecc,inc,Omega,w,nu). % If 9 outputs are asked for, w_true, u_true, and lambda_true will also % be returned. These parameters are important for near equatorial elliptical % orbits, inclined near circular orbits, and near equatorial, near circular % orbits % % a: Semi-major axis of orbit in km % ecc: Eccentricity of orbit % inc: Inclination of orbit in radians % Omega: Right ascension of the ascending node in radians % w: Argument of perigee in radians % nu: True anomaly in radians % w_true: True longitude of periapse in radians if equatorial % elliptical orbit [OPTIONAL] % u_true: Argument of Latitude in radians if orbiit is circular % inclined [OPTIONAL] % lambda_true: True longitude in radians if orbit is equatorial % circular [OPTIONAL] function [a,ecc,inc,Omega,w,nu,w_true,u_true,lambda_true] = elorb(R,V,U) if nargin < 2 || nargin > 4 error('Incorrect number of inputs: see help elorb') elseif nargin == 2 U = 398600.4415; %km^3/s^2 Gravitational Constant of Earth tol = 10^-8; %A tolerance for checking equality elseif nargin == 3 tol = 10^-8; %A tolerance for checking equality end [x,y] = size(R); if y ~= 3 error('Radius vector is not the right size: see help elorb') end if size(R) ~= size(V) error('Velocity and Radius vectors are not the same size. Check inputs') end ecc = zeros(1,x); a = zeros(1,x); w = zeros(1,x); nu = zeros(1,x); Omega = zeros(1,x); inc = zeros(1,x); w_true = zeros(1,x); u_true = zeros(1,x); lambda_true = zeros(1,x); for j = 1:x h = cross(R(j,:),V(j,:)); %Specfic angular momentum vector N = cross([0,0,1],h); %Eccenticity vector e_vec = ((norm(V(j,:))^2 - U/norm(R(j,:)))*R(j,:) - dot(R(j,:),V(j,:))*V(j,:))/U; ecc(j) = norm(e_vec); %Magnitude of eccentricty vector zeta = norm(V(j,:))^2/2 - U/norm(R(j,:)); %Specific mechanical energy of orbit if (1 - abs(ecc(j))) > tol %Checking to see if orbit is parabolic a(j) = -U/(2*zeta); %Semi-major axis P = a(j)*(1-ecc(j)^2); %semi-parameter else P = norm(h)^2/U; %Semi-parameter a(j) = inf; end inc(j) = acos(h(3)/norm(h)); %inclination of orbit in radians Omega(j) = acos(N(1)/norm(N)); %Right ascension of ascending node in radians if N(2) < 0 %Checking for quadrant Omega(j) = 2*pi - Omega; end w(j) = acos(dot(N,e_vec)/(norm(N)*ecc(j))); %Argument of perigee in radians if e_vec(3) < 0 %Checking for quadrant w(j) = 2*pi - w(j); end nu(j) = acos(dot(e_vec,R(j,:))/(ecc(j)*norm(R(j,:)))); %True anomaly in radians if dot(R(j,:),V(j,:)) < 0 %Checking for quadrant nu(j) = 2*pi - nu(j); end %%%%%%%%%%%% Special Cases %%%%%%%%%%%%%%% % Elliptical Equatorial w_true(j) = acos(e_vec(1)/ecc(j)); %True longitude of periapse if e_vec(2) < 0 %Checking for quadrant w_true(j) = 2*pi - w_true(j); end % Circular Inclined u_true(j) = acos(dot(N,R(j,:))/(norm(N)*norm(R(j,:)))); %Argument of Latitude if R(j,3) < 0 %Checking for quadrant u_true(j) = 2*pi - u_true(j); end % Circular Equatorial lambda_true(j) = acos(R(j,1)/norm(R(j,:))); %True Longitude if R(j,2) < 0 %Checking for quadrant lambda_true(j) = 2*pi - lambda_true(j); end end