You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: flightPathDerivative.m
    path of file: ./repos/LADAC/flight_parameters
    
    the code of the file until where you have to start completion: % flightPathDerivative computes the time derivative of the flight-path
% velocity, flight-path angle and flight-path 
%   The time derivative of the flight path quantities (flight path
%   velocity, flight path angle and flight path azimuth) are obtained by
%   deriving their functional definition.
% 
% Literature:
%   [1] Brockhaus, R. et al. (2011): Flugregelung. 3rd ed. Springer-Verlag.
%   [2]	Beyer, Y., Kuzolap, A., Steen, M., Diekmann, J. H., & Fezans, N. 
%   
    
function [ dot_V_K, dot_gamma, dot_chi ] = flightPathDerivative( ...
    V_Kb, dot_V_Kb, M_kb, M_gb, omega_gb_b ) %#codegen

% transform the flight-path acceleration from b to k frame
dot_V_Kk = M_kb * dot_V_Kb;
% the first element is the absolute acceleration (because the other
% elements are zero), see [1, page 212]
dot_V_K = dot_V_Kk(1);

% transform the velocity from b to g frame
V_Kg = M_gb * V_Kb;
% compute the flight-path acceleration in g frame [1, page 213]
dot_V_Kg = M_gb * dot_V_Kb + cross(M_gb*omega_gb_b,V_Kg);

% The flight path azimuth is defined in [1, page 212] or indirectly through
% the definition of M_kg(gamma,chi) in [1, page 58]. The function is
% derived, the result is given in [2, page 10].
dot_chi = (dot_V_Kg(2)*V_Kg(1) - V_Kg(2)*dot_V_Kg(1)) / ...
    (V_Kg(2)^2 + V_Kg(1)^2);

% The flight path angle is defined in [1, page 212] or indirectly through
% the definition of M_kg(gamma,chi) in [1, page 58]. The function is
% derived, the result is given in [2, page 10].
dot_gamma = ( -dot_V_Kg(3) * (V_Kg(1)^2+V_Kg(2)^2) + ...
    V_Kg(3) * ( V_Kg(1)*dot_V_Kg(1) + V_Kg(2)*dot_V_Kg(2) ) ) / ...
    ( (V_Kg(1)^2+V_Kg(2)^2+V_Kg(2)^2) * sqrt(V_Kg(1)^2+V_Kg(2)^2) );

end