# How do I correctly use the Syntax of fmincon?

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I am trying to optimize a flight path. I have the following equations of motions:

dydt=(thrust*sin(alphat)/m*v)-gh*cos(y)-v*cos(y)/(re+h);

dvdt=(thrust*cos(alphat)/m)-Adrag* rhoh*(v^2)/2*m- gh *sin(y);

dhdt=v*sin(y);

dxddt=(re/re+h)*v*cos(y);

dmdt=-propflow;

dwdt=(1/Ix)*thrust*sin(alphat)*rs;

h and v are limited by the final orbit:

hmax=hfinal;

vmax=vfinal;

the downrange x and w are not constrained. I will set the max values of these parameters to a high value, which they will never reach.

m is the parameter that I want to maximize in my final orbit ans the flight path angle y should be equal to 0,because I want my rocket to reach a circular orbit.

Finally my alphat is the thrust vector control variable with which I would like to minimize my mass loss. So I would like fmincon to calculate my function alphat, so that my mass in the final orbit is as high as possible.

The problem is that I dont't understand how to define

A*x=b;

. Could someone here explain me what exactly A, x and b are and how I calculate them??

Thanks

##### 3 Comments

Walter Roberson
on 10 Dec 2018

### Accepted Answer

Matt J
on 10 Dec 2018

If you do not have any linear constraints, then just set them empty

A=[]; b=[];

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