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: velocityAndRateTransform.m
    path of file: ./repos/LADAC/utilities/axes_transformation
    
    the code of the file until where you have to start completion: function [ V_sub, omega_sub ] = velocityAndRateTransform(V_Kb, omega_Kb, R_sub_b, M_xy)

%velocityAndRateTransform computes the velocity on a given Point due to
%angular velocity and translational velocity of of the body-fixed system
%
% Inputs:
%   R_sub_b             position vector of the point P with 3 elements of 
%                       the subsystem in body-fixed system in [m]
%   euler_angles_sub    vector with 3 elements containing the Euler angles
%                       Phi,Theta and Psi angles between subsystem relative
%                       to the body-fixed system, notation in body-fixed
%                       system in [rad]
%
%   V_Kb                velocity of the body-fixed system in [m/s]
%   omega_Kb            angular velocity in the body-fixed [rad/s]
%
% Outputs:
%   V_sub               resulting velocity in the subsystem [m/s]
%   omega_sub           resulting angular velocity in the subsystem [rad/s]
%

% Disclamer:

    
function [ V_sub, omega_sub ] = velocityAndRateTransform(V_Kb, omega_Kb, R_sub_b, M_xy)

%velocityAndRateTransform computes the velocity on a given Point due to
%angular velocity and translational velocity of of the body-fixed system
%
% Inputs:
%   R_sub_b             position vector of the point P with 3 elements of 
%                       the subsystem in body-fixed system in [m]
%   euler_angles_sub    vector with 3 elements containing the Euler angles
%                       Phi,Theta and Psi angles between subsystem relative
%                       to the body-fixed system, notation in body-fixed
%                       system in [rad]
%
%   V_Kb                velocity of the body-fixed system in [m/s]
%   omega_Kb            angular velocity in the body-fixed [rad/s]
%
% Outputs:
%   V_sub               resulting velocity in the subsystem [m/s]
%   omega_sub           resulting angular velocity in the subsystem [rad/s]
%

% Disclamer:
%   SPDX-License-Identifier: GPL-3.0-only
% 
%   Copyright (C) 2020-2022 Fabian Guecker
%   Copyright (C) 2022 TU Braunschweig, Institute of Flight Guidance
% *************************************************************************

V_sub     = M_xy * ( V_Kb + cross(omega_Kb, R_sub_b) );

omega_sub = M_xy * omega_Kb;

end