%% ECI2LVLH - ECI to Curvilinear frame conversion and vice-versa

% Inputs:

% X1: Reference Frame Pos,Vel in ECI

% X2: Object Pos,Vel in ECI if reverse not true

% Object relative Pos,Vel in Curvilinaer frame if reverse true

% reverse: true for converting from LVLH to ECI

% Units: rad, km, sec

% Tolerance: 1e-12

% Author: Bharat Mahajan (https://github.com/princemahajan)

function [ Y ] = ECI2Curv( X1, X2, reverse )

if size(X2,2) ~= 1

disp('ECI2Curv: Second parameter must be a vector/column matrix');

return;

end

% form DCM

rcap = X1(1:3,1)'/norm(X1(1:3));

hvec = cross(X1(1:3,1)',X1(4:6,1)');

hcap = hvec/norm(hvec);

tcap = cross(hcap,rcap);

DCM = [rcap; tcap; hcap];

% Angular velocity In Hill frame of the chief frame (r^2*w = h)

w = [0;0;norm(hvec)/norm(X1(1:3))^2];

if reverse == true

% convert from Curvilinear to Hill's frame

XLVLH = curv2Hill(X2, X1);

% ECI pos

Y(1:3,1) = DCM'*XLVLH(1:3,1) + X1(1:3,1);

% Inertial relative velocity expressed in LVLH

Y(4:6,1) = XLVLH(4:6,1) + cross(w,XLVLH(1:3,1));

% ECI velocity in ECI frame

Y(4:6,1) = DCM'*Y(4:6,1) + X1(4:6,1);

else

% convert from ECI to LVLH

% inertial difference vector

dX = X2 - X1;

% LVLH pos

Y(1:3,1) = DCM*dX(1:3,1);

% LVLH vel

Y(4:6,1) = DCM*dX(4:6,1) - cross(w,Y(1:3,1));

% to curvilinear frame

Y = Hill2curv(Y, X1);

end

end