stumpff.m

function [Cz, Sz] = stumpff(z)
    %% Stumpff Functions
    %
    % Jeremy Penn
    % 22 September 2017
    %
    % Revision:19/10/17
    %
    % function [Cz, Sz] = Stumpff(z)
    %
    % Purpose:  This function calculates the given Stumpff functions.
    % 
    % Inputs:   o z - The argument of the Stumpff function.
    %
    % Outputs:  o Cz - The cosine Stumpff function.
    %           o Sz - The sine Stumpff function.
    %

     if (z > 0)
         Sz = (z^0.5 -sin(z^0.5))/z^1.5;    %C3 Stumpff
         Cz = (1 - cos(z^0.5))/z;           %C2 Stumpff
     elseif (z < 0)
         Sz = (sinh(-z^0.5) - (-z)^0.5)/((-z)^1.5); %C3 Stumpff (negative argument)
         Cz = (cosh(-z^0.5) - 1)/(-z);              %C2 Stumpff (negative argument)
     else
         Sz = 1/6;
         Cz = 0.5;
     end 
end