# Need Help Solving System of ODEs

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Akrant Rai on 18 Nov 2021
Commented: Akrant Rai on 19 Nov 2021
close all; clear all; clc
I wanted to solve these 4 ode(s) and was trying to use ode45, but the output is not what I was expecting, the v is supposed to decrease but it was increasing, the gamma was also supposed to become more negetive but it remained constant. Any idea about where I must be going wrong? Thanks in advance! g=9.81;
z0=10000;
R=6378000;
h0=(R*z0)/(R+z0);
for z=1:10000
h(z)=(R.*z)./(R+z);
rho0=0.4135;
H=8500;
rho=rho0.*exp((h0-h)./H);
end
v0=450;
gamma0=-20;
m0=2500;
T=15000;
Isp=300;
dodt=@(t,W)[(-g*sin(W(2)))-(T/W(4));(-g/W(1))*cos(W(2));W(1)*sin(W(2));-T/(g*Isp)];
[t,W]=ode45(dodt,[0,21.93],[v0,gamma0,z0,m0])
v=W(:,1);
gamma=W(:,2);
z=W(:,3);
m=W(:,4);

Alan Stevens on 18 Nov 2021
You haven't included the first term on the right-hand side of your equation for dV/dt, nor for dgamma/dt.
Akrant Rai on 19 Nov 2021
Alright. I will check the physics again to make sure that is right. Thank you for all the help!

R2020b

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