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# Simple rocket vehicle dynamics

Assumptions: Vertical trajectory,constant gravitational acceleration and atmospheric drag is neglected

```clc;
clear all;
g0  = 9.81;      % [km/s^2] Constant at its sea-level value
m0  = 30000;     % [kg] Initial mass
n  = 13;        % Mass ratio
Isp = 320;       % [s] Specific impulse
T   = 900000;    % [N] Thrust

mf = m0/n;        % The burnout mass
md = T/(Isp*g0);  % Propellant mass flow rate
t_burn = (m0 - mf)/md;  % The time until burnout

V_ex = Isp*g0;    % Exhaust velocity
h_burn = V_ex/md*(mf*log(mf/m0) + m0 - mf) - 0.5*t_burn^2*g0;
v_burn = V_ex*log(m0/mf) -g0*t_burn;
h_max = 0.5*V_ex^2/g0*log(n)^2 - V_ex*m0/md*(n*log(n)- n + 1)/n;

fprintf('The time until burnout  %4.2f [s] \n', t_burn);
fprintf('The burnout altitude    %4.2f [km] \n', h_burn/1000);
fprintf('The burnout velocity    %4.2f [km/s] \n', v_burn/1000);
fprintf('TThe maximum altitude   %4.2f [km] \n', h_max/1000);
% Look for the next post where we will present more acurate calculations
% considering the gravity effects and atmospheric drag.```
```The time until burnout  96.59 [s]
The burnout altitude    192.64 [km]
The burnout velocity    7.10 [km/s]
TThe maximum altitude   2765.10 [km]```

Equations from Orbital Mechanics for Engineering Students,Second Edition,Aerospace Engineering