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I've formulated a method for modeling the flight of a rocket projectile. Can anyone read it over and point out any mistakes false assumptions, etc? thanks!
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For every reasonable definition of m and a (which is missing), this is wrong.According to Newton’s Second Law, the product ma must remain constant.
Not necessarily, R does not have to be constant.Since its acceleration is changing over time
You solved a differential equation before, where is the problem with setting up another?Thus, this system leads to a seemingly circular and unresolvable issue.
hmm, you're right. I should have done the derivation purely in terms of momentum.For every reasonable definition of m and a (which is missing), this is wrong.
Well, I was assuming a constant R.Not necessarily, R does not have to be constant.
Δm in the integral has a different meaning compared to above, but uses the same symbol.
Air resistance depends on the velocity and the direction of motion, you cannot integrate it like that (with both meanings for integrate).
Why does alpha depend on the position of the rocket?
I don't know any methods for solving an ODE containing an unknown function (the angle of attack). I tried many ways to get an explicit equation of velocity and angle of attack, but I didn't succeed. I don't believe there is a way to avoid the implicit nature of the system. Thus the approximation algorithm.You solved a differential equation before, where is the problem with setting up another?
The iteration does not work like that. It gives something like an arc, but not the correct results.
That assumption should appear somewhere then. For most rockets, it is not true.Well, I was assuming a constant R.
In the equation with the integral, in the denominator.There is no delta m in the integral.
That is a reasonable approximation, but it is unrelated to my point. The acceleration from air resistance is not constant in time, so its contribution to velocity is not proportional to time.I guess I just assumed that air resistance was always antiparallel to direction of motion.
Sure, but alpha cannot be calculated based on position values relative to the starting point or some other fixed reference.Alpha can depend either on position or on time. Either way its an unknown function.
Every differential equation has at least one unknown function. Sure, alpha will couple the two equations for the directions (a realistic treatment of air resistance will do the same) and probably make an analytic solution impossible, but you can get the iteration steps out of this differential equation.I don't know any methods for solving an ODE containing an unknown function (the angle of attack)
In its current version, I would not use it for any predictions. To know "oh well, the rocket will go up and forwards and then fall down again" you don't need calculations, and I don't think it is more precise than that.Is it too far off to even be an approximation?
I meant that. What do you mean by the iteration steps though?Every differential equation has at least one unknown function. Sure, alpha will couple the two equations for the directions (a realistic treatment of air resistance will do the same) and probably make an analytic solution impossible, but you can get the iteration steps out of this differential equation.
The same thing as you when you calculate the position in steps of 0.5 seconds.I meant that. What do you mean by the iteration steps though?