Change in velocity equation with explicit method

Question

BioZ 2020-3-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/513659-change-in-velocity-equation-with-explicit-method

回答： Ameer Hamza 2020-3-29

采纳的回答： Ameer Hamza

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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.

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darova 2020-3-29

Can you explain more? You have

constant. What are you trying to calculate? What is V?

BioZ 2020-3-29

编辑：BioZ 2020-3-29

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.

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.

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Answer 1

Ameer Hamza 2020-3-29

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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

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Answer 2

darova 2020-3-29

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https://ww2.mathworks.cn/matlabcentral/answers/513659-change-in-velocity-equation-with-explicit-method#answer_422715

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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