CRes3BP_EOM.m

%{
...
This is the Equation of Motion of the CR3BP

Created on feb 20 2020 15:50
...
%}

function X_Dot = CRes3BP_EOM(t,X,mu)


if length(X)>4
type = 'ThreeDim';
else
    type = 'Planar';
end


switch type 
    case 'Planar'
        % Unpack the state variables
x = X(1);
y = X(2);


mu1 = 1-mu; % mass of larger  primary (nearest origin on left)
mu2 =   mu; % mass of smaller primary (furthest from origin on right)

% The Distances from the larger and Smaller Primary
d3= ((x+mu2)^2 + y^2)^1.5;    
r3= ((x-mu1)^2 + y^2 )^1.5;

% Partial Derivative of the Pseudo Potential Function
Ux =  x - mu1*(x+mu2)/d3 - mu2*(x-mu1)/r3 ;
Uy =  y - mu1* y     /d3 - mu2* y     /r3 ;




xDot  = X(3);
yDot  = X(4);

xDDot = 2*yDot + Ux;
yDDot = -2*xDot + Uy;


X_Dot = [xDot;yDot;xDDot;yDDot];

%============================================================================
    case 'ThreeDim'
% Unpack the state variables
x = X(1);
y = X(2);
z = X(3);


mu1 = 1-mu; % mass of larger  primary (nearest origin on left)
mu2 =   mu; % mass of smaller primary (furthest from origin on right)

% The Distances from the larger and Smaller Primary
d3= ((x+mu2)^2 + y^2 + z^2)^1.5;    % P3 and larger primary
r3= ((x-mu1)^2 + y^2 + z^2 )^1.5;   % P3 and larger primary

% Partial Derivative of the Pseudo Potential Function
Ux =  x - mu1*(x+mu2)/d3 - mu2*(x-mu1)/r3 ;
Uy =  y - mu1* y     /d3 - mu2* y     /r3 ;
Uz = -mu1*z/d3 - mu2*z/r3;




xDot  = X(4);
yDot  = X(5);
zDot  = X(6);
xDDot = 2*yDot + Ux;
yDDot = -2*xDot + Uy;
zDDot = Uz;



X_Dot = [xDot;yDot;zDot;xDDot;yDDot;zDDot];


end