output of the function used in ode113

I am using the 'ode113' function to integrate my state (6x1) for 1 second using the function 'derivative' .

I want to extract the last value of the 'Xdot' calculated by the 'ode113', is there any way to do that ?

options  = odeset('RelTol',1e-13,'AbsTol',1e-16);
[~ , listState] = ode113(@(t, state)derivative(t, state, GM) , [0 1] , state, options);
newState = listState(end,:);
% Xdot = ?!
function Xdot = derivative(~, X, GM)
r    = norm(X(1:3));
Xdot = [X(4:6); -GM * X(1:3) / r^3];
end

Answer 1

[Hassaan]

Integrates a state using ode113 and then extracts the last value of Xdot calculated by ode113 using the derivative function. Note that you need to have defined your initial state vector state and the parameter GM before running this code.

% Options for ODE solver
options = odeset('RelTol',1e-13,'AbsTol',1e-16);

% Define the initial state and the parameter GM
% Replace these with your actual initial conditions and GM value
state = [initial_position_and_velocity]; % Example: [x0, y0, z0, vx0, vy0, vz0]
GM = your_GM_value; % Gravitational constant times the mass of the central body

% Integrate the system of equations from t = 0 to t = 1 second
[t, listState] = ode113(@(t, state) derivative(t, state, GM), [0 1], state, options);

% Extract the last state from the output
newState = listState(end,:);

% Calculate the last derivative using the derivative function with the last state
% and the last time point
Xdot_last = derivative(t(end), newState, GM);

% Display the last derivative
disp('The last Xdot value is:');
disp(Xdot_last);

% Define the derivative function
function Xdot = derivative(~, X, GM)
    r = norm(X(1:3)); % Calculate the radial distance
    % Calculate the derivative of the state vector
    Xdot = [X(4:6); -GM * X(1:3) / r^3];
end

% Continue with the rest of your code...

• initial_position_and_velocity should be replaced with the actual initial state vector of your system, which is a six-element vector consisting of the initial position and velocity components.
• your_GM_value should be replaced with the actual value of the gravitational parameter (gravitational constant times the mass of the central body) for your problem.

The derivative function which calculates the rate of change of the state vector based on the current state and the gravitational parameter GM. The Xdot_last variable will contain the rate of change at the last time step after the integration is complete. Make sure that your state and GM variables are defined before running this code.

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