calculate the speed and position of the rocket and plot a graph of velocity vs time and altitude vs time

1::: m*dV/dt= v_e*dm/dt -G*Mm/r^2 -0.5ρAV^2 C_d

2::: ρ=1.225*10^(-3h/50000)

i need to plot a graph of speed against time using equation 1. I am not allowed to use matlab function to solve the differential eqaution such as ode45, or dsolve instead i need to use explicit method. Also I need to plot a graph of altitude against time

This is my code so far

I am stuck and don't know what to do next? please help

clear

speed(1)=v;
speed_2(1)=v;
height(1)=h;
height_2(1)=h;
mass(1)=m_0;
radii(1)=R;
rho(1)=rho_0;
drag(1)=D;
thrust(1)=T;
weight(1)=w_0;

%CONSTANTS
G=6.67408*10^(-11);
M=5.9722*10^(24);
R=6371000;
gravity= 9.81;
A= 75;
c_d=0.4;
v_e=4500;
dt=1;
m_e=54000;
m_0=894000;
dm=5000;
dm_2=0;
tNfuel=(m_0/m_e)/dm;


%INITAL VALUE AT t=0
v=0;
r=R;
h=0;
rho_0=1.225;
D=0;
T=0;
w_0=(G*M*m_0)/(R^2);

%GIVEN EQUATION 
for i=2:lenght(t)
    
    rho(i)=1.225(1)*10^((-3*h(i-1)/50000);
    
    if m(i-1)>=m_e
        m(i)=m(i-1)- dm*dt;
    else
        m(1)=m(i-1);
        dm=0;
    end
  
 
   
end

plot(v,t)

Answer 1

[Ameer Hamza]

It seems like you are trying to use Euler's method. If you are confused about implementing the numerical ODE solver from scratch, then look at the code of ode1.m, which is an old MATLAB solver based on the Euler method: https://www.mathworks.com/matlabcentral/answers/98293-is-there-a-fixed-step-ordinary-differential-equation-ode-solver-in-matlab-8-0-r2012b. It is no longer available in MATLAB. You can adapt according to your ODEs.

Answer 2

[Image Analyst]

My attached demo gives you all kinds of control over initial parameters, and computes just about every possible thing you could want to know about a projectile. Numerous graphs are plotted. Adapt as needed.

Answer 3

[MUTHUKUMAR K]

%CONSTANTS
G=6.67408/10^11;
M=5.9722*10^24;
R=6371000;
gravity= 9.81;
A= 75;
c_d=0.4;
v_e=4500;
dt=1;
m_e=54000;
m_0=894000;
dm=5000;
dm_2=0;
tNfuel=(m_0/m_e)/dm;

%INITAL VALUE AT t=0
v=0.3;
r=R;
h=0;
rho_0=1.225;
D=0;
T=0;
w_0=(G*M*m_0)/(R^2);
t=6;

%clear


speed(1)=v;
speed_2(1)=v;
height(1)=h;
height_2(1)=h;
mass(1)=m_0;
radii(1)=R;
rho(1)=rho_0;
drag(1)=D;
thrust(1)=T;
weight(1)=w_0;




%GIVEN EQUATION 
for i=2:length(t)
    b=(-3*h(i-1)/50000)
rho(i)=1.225*(1)*10^b;
    
    if b(i-1)>=m_e
        G(i)=U(i-1)-(dm*dt);
    else
        M(1)=M(i-1);
        dm=0;
    end
    plot(v,t(i,:));
    hold on 
end
ax=gca;
ax.XAxisLocation='origin'
ax.YAxisLocation='origin'
xlabel('v');
ylabel('t');
title('V-T');
grid on;
grid minor;
hold off;