# Solving Rocket Launch Differential Equations

#### mysticboon

Hi I'm currently working on a project which involves solving the rocket launch differential equations to find the apogee of an orbit. I know the analytical model for the equations as:
Δu = Isp*g0*ln(mf/me), where Isp is fuel impusle, mf is mass of full tank and me is mass of empty tank, but for this project I need to solve the differential equations in matlab numerically.

I know the general equation as d(M*u)/dt = Fnet = Isp*g0*dmp/dt where dmp is the change in mass of the propellant. I'm just kind of stuck in working around the differential equations to get something I can solve for in matlab. I've tried substituting some differentials for each other in order to get one equation, but I ended up cancelling terms to get something that doesn't make sense to me. I've been using this site to work with the equations: http://exploration.grc.nasa.gov/education/rocket/rktpow.html
Code:
% Veq = Isp*g0
% mdot = F/(Isp*g0)
% mdot = dmp/dt
% Mdu = Veq*mdot
% dm = -dmp = -mdot = -F/(Isp*g0)
% dmp = fnet/veq = fnet/(Isp*go)
% du = -(Isp(g0)*fnet/(Isp*g0)/M
Can anyone please give me some help in how to get one or two differential equations to use in matlab? Thank you

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