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Juanka
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Homework Statement
Assume you have a spacecraft capable of a constant thrust (T) mission. The spacecraft ’s electric thruster has an efficiency given by Eff= 1-(((Isp-5000)^2)/(5000^2)) , where Isp is the specific impulse, in seconds. The power supply mass is given by
Mp=(alpha*g*T*Isp)/(2*Eff). The propellant mass is given by dM=Mo*(1-exp(-dV/(Isp*g))), where mo is the initial total spacecraft mass. dV=1.4*104m/s, g=9.81m/s2, T=0.3N, Mo=50000kg, and alpha=10kW/kg. Determine the optimum specific impulse, Iopt (where (Δm+mp) is at a minimum) for Isp =0..10000s.
(Hint: You will be taking the derivative of (dM+mp) with respect to Isp, then use optimization to determine Iopt.)
The Attempt at a Solution
First of all, I understand I have to add the dM and Mp equations together and take the derevidive respect to Isp. I think I should use the a form of the
Code:
simplify(dsolve('DIsp=dM+mp,'y(0)=?','Isp'))
Also do I wait until I have found the Derivative to input the given definitions of each variable or should I do that last?