Integration Method

[D0c78]

Hello,
I have been having doubts on which integration method is being used by 42 for the propagation, and I was wandering how to select it if possible.

I have used 42 to propagate the attitude of a satellite in free motion (fixed orbit) with the aim to compare the outputs to those from a model I wrote and my verify results.
I though that the RK4 was being used, but after not getting the same results with the same time step (1sec), I did some digging and found out the way I had 42 set up ended up using an order 1 method, which seemed off, since I only see RK4 mentioned in the code.

May I ask for some elucidation on this matter?

Thank you in advance.

Regards,
Davide

[ericstoneking]

Hi Davide,

By "order 1 method", do you mean the ORDER_N option (else GAUSS_ELIM) in your SC_foo.txt input file? These two options differ in how they construct the equations of motion, but both methods propagate using RK4. I suspect you have something else going on.

Regards,
-Eric

PS. GAUSS_ELIM and ORDER_N should both give you the same answer to essentially machine precision.

[D0c78]

Hi Eric,
thank you for responding.

What I mean by "order 1 method" is the order of the polynomial that describes the global truncation error (or maximum error across the simulation) of the method as a function of the time step size used.
So that in practice, an Euler method would have max_error(dt) = K_a*dt^(1) and for RK4 max_error(dt) = K_b*dt^(4).

To verify this I used a reference simulation that used fixed step (ts=0.005s) ode8 from matlab. I then compared the error I got w.r.t. this reference against the time step used with 42. From that I got a first order relationship (max_error(dt) = K_a*dt^(1)).

However...I'd expect a 4th order...
I verified what method was used for building the dynamic equations in my SC_* file : GAUSS_ELIM. I agree that changing this to ORDER_N does not change the results (to machine precision), I have also verified this.

I guess I am missing something, I leave the files listed below as example of what I am doing with 42, where the only changes I made have been for the simulation step size and the dynamics method used:

• Inp_Sim.txt
• Orb_LEO_SSO.txt
• SC_SAT_010.txt

Look forward to hear if you have any suggestions.

Regards,
Davide

[ericstoneking]

Hi Davide,

I'm going with the utterly predictable question: how well do you trust your reference sim? It may be that you have dynamics modeled in one that is not modeled the same in the other. If it turns out that you've uncovered a flaw in my RK4 implementation(s), please do let me know. Till then, good luck in your exploration.

Regards,
-Eric

[D0c78]

Hi Eric,
Thank you again for replying. It is not surprising that my sim is being questioned, everything I am doing is ultimately because I want to verify my work, so a mistake of mine is surely an open option.

I would like to raise a question about managing the gravity gradient torques: most of the difference I found is when I include this perturbations. The torque definition should match with the code in 42, but I am wandering if I set up the case correctly.
I aim to only include the gravity gradient torque caused by the Earth central field and not include the one from the Moon, so I wrote the line in Inp_Sim.txt, under "Celestial Bodies of Interest" as follows:
TRUE FALSE ! Earth and Luna
My doubt is if I am correctly excluding the "Luna" influence with this, since in the example code Earth and Luna seem to be treated together. If not, this would explain a certain discrepancy, since I have not included the gravity gradient torque from the Moon in my models.

Looking forward to any suggestion.

Regards,
Davide