Example_5_02.m

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Example_5_02
% ~~~~~~~~~~~~
%{
  This program uses Algorithm 5.2 to solve Lambert's problem for the
  data provided in Example 5.2.
 
  deg    - factor for converting between degrees and radians
  pi     - 3.1415926...
  mu     - gravitational parameter (km^3/s^2)
  r1, r2 - initial and final position vectors (km)
  dt     - time between r1 and r2 (s)
  string - = 'pro' if the orbit is prograde
           = 'retro if the orbit is retrograde
  v1, v2 - initial and final velocity vectors (km/s)
  coe    - orbital elements [h e RA incl w TA a]
           where h    = angular momentum (km^2/s)
                 e    = eccentricity
                 RA   = right ascension of the ascending node (rad)
                 incl = orbit inclination (rad)
                 w    = argument of perigee (rad)
                 TA   = true anomaly (rad)
                 a    = semimajor axis (km)
  TA1    - Initial true anomaly (rad)
  TA2    - Final true anomaly (rad)
  T      - period of an elliptic orbit (s)

  User M-functions required: lambert, coe_from_sv
%}
% ---------------------------------------------

clear all; clc
global mu
deg = pi/180;

%...Data declaration for Example 5.2:
mu     = 398600;
r1     = [  5000  10000  2100];
r2     = [-14600   2500  7000];
dt     = 3600;
string = 'pro';
%...

%...Algorithm 5.2:
[v1, v2] = lambert(r1, r2, dt, string);

%...Algorithm 4.1 (using r1 and v1):
coe      = coe_from_sv(r1, v1, mu);
%...Save the initial true anomaly:
TA1      = coe(6);

%...Algorithm 4.1 (using r2 and v2):
coe      = coe_from_sv(r2, v2, mu);
%...Save the final true anomaly:
TA2      = coe(6);

%...Echo the input data and output the results to the command window:
fprintf('-----------------------------------------------------')		
fprintf('\n Example 5.2: Lambert''s Problem\n')
fprintf('\n\n Input data:\n');
fprintf('\n   Gravitational parameter (km^3/s^2) = %g\n', mu);
fprintf('\n   r1 (km)                       = [%g  %g  %g]', ...
                                            r1(1), r1(2), r1(3))
fprintf('\n   r2 (km)                       = [%g  %g  %g]', ...
                                            r2(1), r2(2), r2(3))
fprintf('\n   Elapsed time (s)              = %g', dt);
fprintf('\n\n Solution:\n')

fprintf('\n   v1 (km/s)                     = [%g  %g  %g]', ...
                                            v1(1), v1(2), v1(3))
fprintf('\n   v2 (km/s)                     = [%g  %g  %g]', ...
                                            v2(1), v2(2), v2(3))
																							 
fprintf('\n\n Orbital elements:')
fprintf('\n   Angular momentum (km^2/s)     = %g', coe(1))
fprintf('\n   Eccentricity                  = %g', coe(2))
fprintf('\n   Inclination (deg)             = %g', coe(4)/deg)
fprintf('\n   RA of ascending node (deg)    = %g', coe(3)/deg)
fprintf('\n   Argument of perigee (deg)     = %g', coe(5)/deg)
fprintf('\n   True anomaly initial (deg)    = %g', TA1/deg)
fprintf('\n   True anomaly final   (deg)    = %g', TA2/deg)
fprintf('\n   Semimajor axis (km)           = %g', coe(7))
fprintf('\n   Periapse radius (km)          = %g', coe(1)^2/mu/(1 + coe(2)))
%...If the orbit is an ellipse, output its period:
if coe(2)<1
	T = 2*pi/sqrt(mu)*coe(7)^1.5; 
	fprintf('\n   Period:')
	fprintf('\n     Seconds                     = %g', T) 
	fprintf('\n     Minutes                     = %g', T/60)
	fprintf('\n     Hours                       = %g', T/3600)
	fprintf('\n     Days                        = %g', T/24/3600)
end
fprintf('\n-----------------------------------------------------\n')		
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~