# Recommended ML toolbox for complex spaceship braking optimization.

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Isak Ederlöv on 14 Apr 2022
Answered: Alan Weiss on 14 Apr 2022
I am working on a big project where my team and I have developed a mathematical model based on differential equations to simulate the flight path of a spacecraft modeled as just a ballistic projectile with constant cD. What we want is to be able to land anywhere on earth from orbit, using only a braking motor. The complexity of air resistance and coriolis makes it seemingly impossible (for us at least) to do this analytically, and my question is how would one go about this using one of the ML toolboxes (or is it a bad approach from the start)? Simulations take only seconds and we have weeks so we have practically unlimited training data.
Our variables are braking force and time and duration of the braking, for a given initial orbital state. I understand this is a very broad and difficult question, but if anyone could pitch in with just any helpful hint or idea of which toolbox or method could be useful, it would be greatly, greatly appreciated.

Alan Weiss on 14 Apr 2022
You might be able to use some Optimization Toolbox solvers. There is one (laughably simplified, but still) relevant example here:
Discretized Optimal Trajectory, Problem-Based (incomplete model of air resistance, no account taken of varying mass as rocket fires)
There are other examples showing how to use an ODE solution to optimize something:
Optimize an ODE in Parallel (not a trajectory model, but you can put in your own ODE here. Uses Global solvers, but you can use fmincon successfully, just be careful about finite differences as explained in Optimizing a Simulation or Ordinary Differential Equation)
There are other ODE optimization examples, too, for curve fitting but the same considerations apply to optimizing a trajectory:
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation

R2021b

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