# Solving Equations of motion with ode15s

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Brendan Görres on 3 May 2019
Commented: Torsten on 6 May 2019
Recently I am trying to solve a system of equations with ode15s. The goal is to calculate the Ascent trajectory of a Rocket with a control variable alpha, which is the angle between the velocity vector v and the thrust vector, so that by changing alpha manually I should change the flight direction.
%Thrust vector control variable
alpha=(-2*pi/180)
%alpha=(-2*pi/180)*t+10
%functions
gh=g0*((re/h)^2);%Gravi*tationsbeschleunigung abh. von h
rhoh=rho0*exp(-h/sh);%Luftdichte abh. von h
%EoM
dydt=(thrust*sin(alpha)/m*v)-(v*cos(y)/h)-gh*cos(y);
dhdt=v*sin(y);
dxddt=(re/h)*v*cos(y);
dmdt=-propflow;
dwdt=(1/Ix)*thrust*sin(alpha)*rs;
in a first run I assume alpha to be konstant and I experimented a little bit with the value (so for example alpha=-2*... and in the next run alpha= +10*...). In a next step I assumed alpha to be linear so for example
alpha=(-2*pi/180)*t+10
and in a last step I assumed it to be quadratic:
alpha=0.5*(-2*pi/180)*t^2+10*t+0.01
I am using ode15s to solve the equations, because my code needs to include the algebraic variable t.
I plotted the results over t and I receive the exact same plots for every single run, regardless of alpha being konstant linear or quadratic.
How is that possible?
Torsten on 6 May 2019
And the values you get for the variables look realistic to you ? E.g. a velocity of 12000 m/s ?
I suggest you reinspect your equations first before going into details about the setting of "alpha".