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So, I ve been trying to add orientation to my model of the flight dynamics of a rocket but I ve been running into a lot of problems. I didn't bother actually doing the math for the moments of inertia and everything because I guess it really doesn't have that much of an effect on the general behaviour of the rocket,but rather simple specifics of its movement.

The problem is the following, when the rocket is offset from a perfect 90 degree angle at launch, it gains horizontal velocity faster than vertical (due to gravity) and therefore acquires another offset from the launch angle (say it was 89 degrees). The fins of the rocket should stabilize it by using the lift gained from the small angle of attack and point it back towards the velocity vector, this is what produces the gravity turn we all know and love (I think, I might be wrong though). In my model though, the rocket fails to stabilize properly and starts rotating uncontrollably after a certain amount of time.

At first it oscillates as a pendulum would,but deviating just a bit more with each period and gaining more and more angular velocity. Is this something that naturally arises when using euler's method to analyse this type of motion or would it also happen if I were to use Runge-Kutta's? I was thinking it may be something that naturally happens when using discrete time to analyse something that would be continous. By reducing the time step I was able to increase the time it would take for the deadly rotation to take place, but I am running out of memory on excel (Its waay easier than using MATLAB or anything else, at least for me). I am going to be trying to use 2nd order RK and see if it works.

Anyways, please tell me what you think, I am attaching the excel spreadsheet and a picture with the equations I am trying to approximate

https://www.mediafire.com/?led0x2ubszo7avv

http://imgur.com/4I3cFUB

Thanks a lot!

The problem is the following, when the rocket is offset from a perfect 90 degree angle at launch, it gains horizontal velocity faster than vertical (due to gravity) and therefore acquires another offset from the launch angle (say it was 89 degrees). The fins of the rocket should stabilize it by using the lift gained from the small angle of attack and point it back towards the velocity vector, this is what produces the gravity turn we all know and love (I think, I might be wrong though). In my model though, the rocket fails to stabilize properly and starts rotating uncontrollably after a certain amount of time.

At first it oscillates as a pendulum would,but deviating just a bit more with each period and gaining more and more angular velocity. Is this something that naturally arises when using euler's method to analyse this type of motion or would it also happen if I were to use Runge-Kutta's? I was thinking it may be something that naturally happens when using discrete time to analyse something that would be continous. By reducing the time step I was able to increase the time it would take for the deadly rotation to take place, but I am running out of memory on excel (Its waay easier than using MATLAB or anything else, at least for me). I am going to be trying to use 2nd order RK and see if it works.

Anyways, please tell me what you think, I am attaching the excel spreadsheet and a picture with the equations I am trying to approximate

https://www.mediafire.com/?led0x2ubszo7avv

http://imgur.com/4I3cFUB

Thanks a lot!