MATLAB Derivative

Question

John 2011-4-20

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/5846-matlab-derivative

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 (?m+mp) is at a minimum) for Isp =0..10000s.

I need to take the derivative of (dM+mp) with respect to Isp, then use optimization to determine Iopt.

simplify(dsolve('DIsp=dM+mp,'y(0)=???','Isp'))

However I do not know what my initial condition should be. Also I think I may have to solve the equations for Isp? am i on the right track and suggestions please.

Also do I wait until I have found the Derivative to input the given definitions of each variable or should I do that last?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

John 2011-4-20

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/5846-matlab-derivative#answer_8156

在 MATLAB Online 中打开

So I have been playing with code and I have came up with the following:

%%Given Definitions
dV=1.4*10^4; %units are in m/s
g=9.81;%units are in m/s^2
T=0.3;% units are in N
Mo=50000;% units are in kg
alpha= 10/1000; %units are in kg/W
%Isp=.1;
%%Given Equations
Eff=@(Isp) 1-(((Isp-5000)^2)/(5000^2)); 
Mp=@(Isp, Eff) (alpha*g*T*Isp)/(2*Eff);     
dM=@(Isp) Mo*(1-exp(-dV/(Isp*g)));
%%Analytical Soultion
syms Isp
diff((alpha*g*T*Isp)/(2*(1-(((Isp-5000)^2)/(5000^2)))) + Mo*(1-exp(-dV/(Isp*g))))