Change in velocity equation with explicit method
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Hello Everyone, I am new to MatLab, and looking for some help.
I have a code where I have 3600 time steps.
I am calculating change in mass of a rocket every step which is assumed to be constant (5000kg/s)
with this bit of a code
for n=2:length(t)
if M(n-1) >= mass_r;
M(n)=M(n-1)-dm*dt;
else
M(n)=mass_r-1;
end
end
I would like someone to help me to implement this equation in MatLab form
I tried using an explicit method but alot of errors just rainfalls on me.
Would appreciate any help.
2 个评论
darova
2020-3-29
Can you explain more? You have 
constant. What are you trying to calculate? What is V?
constant. What are you trying to calculate? What is V?V is the velocity, I can't express this equation using the explicit method discretisation.
The Idea is to calculate velocity on each time step.
For example if ve have this simple equation 
and initial value 
We can rewrite the equation and approximate it into this form 
and from this simply with the use of explicit method we can get this form 
which would work perfectly in MatLab.
and initial value We can rewrite the equation and approximate it into this form and from this simply with the use of explicit method we can get this form which would work perfectly in MatLab.I just need help with the equation stated in the question to rewrite it for use in MatLab by using explicit method discretisation to calculate velocity at each time step.
Would appreciate any help.
采纳的回答
Ameer Hamza
2020-3-29
See this solution by using ode45
[t, V] = ode45(@dV, [0 300], 0);
plot(t,V)
function dVdt = dV(t, V)
G = 6.67408e-11;
M = 5.9722e24;
R = 6371e3;
A = 75;
Cd = 0.4;
me = 54000;
mo = 894000;
ve = 4500;
dmdt = 5000;
m_fuel = mo - me;
time_fuel = m_fuel/dmdt;
if t < time_fuel
m = mo - t*dmdt;
else
m = me;
end
dVdt = 1/m*(ve*dmdt - G*M*m/R^2 - 0.5*Cd*A*V^2);
end
更多回答（1 个）
darova
2020-3-29
Here is what i think about this question
for n = 2:length(t)
if m(n-1) > me % if rocket has fuel
dm = 5000;
else
dm = 0; % no fuel, mass change=0
end
dV = (ve*dm - ...)/m % longformula for acceleration
m(n) = m(n) - dm*dt; % mass change
V(n) = V(n-1) + dV*dt;
end
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