Printing all outputs of the function that has been solved via ode45

I have defined a function to be solved using ode45. The function is called endoFlightDeriv

function [deriv, m, h] = endoFlightDeriv(t, X, E, L,phaseCode)

Then I solve it using ode45

[time_vert,sol_vert]=ode45(@(t,x)endoFlightDeriv(t,x,E,L,PhaseCode),tspan,x0,options)

My question is, how can I output the values of m and h at each integration step?

This is the first question that I ever post, so I apologize in advance if this is not clearly stated. Obviously I can further explain my problem.

[Sam Chak]

Hi @Niccolo Carioli,

It appears to be an endo-atmospheric flight mission. My assumption is that 'm' represents the mass of the vehicle, while 'h' denotes the height of the vehicle. Is the system described in linear state-space?

Could you please show the output functions 'm' and 'h'? It would be beneficial to understand the parameters and state variables that are involved in these functions.

[Niccolo Carioli]

Can you explain better? However @stephen23 answered to my problem

[Sam Chak]

No worries. I believe your specific technical issue in MATLAB has been resolved and closed. However, it's worth noting that there are at least six approaches available to achieve this, depending on the complexity of the output functions involved.

[Niccolo Carioli]

Your statement is indeed correct. This is a code for the simulation of the endoatmospheric trajectory of a launcher. However this is not written in a state space notation, the function simply defines the vectorial equation of motion to be solved. The mass is a scalar and its change it's computed using the flow rate and the time

Answer 1

[Stephen23]

This questions gets asked regularly on this forum: users often imagine that there must be some easy way to get some values out of the function when it is being solved by ODE45 (or whatever solver they are using). In practice it is not that simple: ODE solvers may take arbitrarily small steps or even steps backwards... it is not a trivial task to figure out which function calls produce data which correspond to the values returned by the ODE solver... in fact this task is quite difficult.

Thus in most cases it is much simpler to just call the function after the ODE solver has finished, using the values obtained by the ODE solver. A simple loop and calling the function usually is sufficient.

[Niccolo Carioli]

That make sense, thank you!

Answer 2

[Torsten]

Assuming m and h are scalars, use

[time_vert,sol_vert]=ode45(@(t,x)endoFlightDeriv(t,x,E,L,PhaseCode),tspan,x0,options)
for i = 1:numel(time_vert)
    [~, m(i), h(i)] = endoFlightDeriv(time_vert(i), sol_vert(i,:), E, L,phaseCode)
end

If not, change the loop appropriately.

[Niccolo Carioli]

Perfect!