Solve function unable to compute algebraic system of equations

Hello, I am trying to solve this system of 4 equations using the solve function, however MATLAB is saying that it cannot find an explicit solution.

clc
clear all

%syms a b c d
syms ms1 mp1 ms2 mp2

g=9.8
isp1=290
isp2=320

for deltav1=5000       %%%guess
deltav2=9500-deltav1

e1=isp1*g*log((3000+ms1+mp1+ms2+mp2)/(3000+ms1+mp1+mp2))
e2=isp2*g*log((3000+ms2+mp2)/(3000+ms2))
e3=mp1/(ms1+mp1)
e4=mp2/(3000+ms2+mp2)


ans=solve(e1==deltav1, e2==deltav2, e3==0.9, e4==0.8)

end

There are four equations and four unknowns so I don't understand what the problem is. I am on MATLAB R2019B.

Any help or suggestions is greatly appreciated.

Answer 1

[Walter Roberson]

syms ms1 mp1 ms2 mp2
g=9.8

g = 9.8000

isp1=290

isp1 = 290

isp2=320

isp2 = 320

deltav1=5000       %%%guess

deltav1 = 5000

deltav2=9500-deltav1

deltav2 = 4500

e1=isp1*g*log((3000+ms1+mp1+ms2+mp2)/(3000+ms1+mp1+mp2))

e1 = 

e2=isp2*g*log((3000+ms2+mp2)/(3000+ms2))

e2 = 

e3=mp1/(ms1+mp1)

e3 = 

e4=mp2/(3000+ms2+mp2)

e4 = 

eqn = [e1==deltav1, e2==deltav2, e3==0.9, e4==0.8].'

eqn = 

partial_mp1 = solve(eqn(1), mp1)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

partial_mp1 = 

eqn2 = subs(eqn(2:end), mp1, partial_mp1)

eqn2 = 

partial_mp2 = solve(eqn2(1), mp2)

partial_mp2 = 

eqn3 = subs(eqn2(2:end), mp2, partial_mp2)

eqn3 = 

partial_ms1 = solve(eqn3(1), ms1)

partial_ms1 = 

eqn4 = subs(eqn3(2:end), ms1, partial_ms1)

eqn4 = 

simplify(lhs(eqn4)) == rhs(eqn4)

ans = 

Which is to say that if you solve the first three equations for mp1 mp2 ms1 then the 4th equation becomes inconsistent. There are no solutions to the equations.

[Andrew Nguyen]

Hi walter, thank you for your response. In this case, the goal is to iterate delta v1 and thus delta v2 in order to find a solution that will work. Is there any way I could do this?

[Torsten]

syms ms1 mp1 ms2 mp2 deltav1 deltav2
g=9.8;
isp1=290;
isp2=320;
%deltav1=5000       %%%guess
deltav2=9500-deltav1;
e1=isp1*g*log((3000+ms1+mp1+ms2+mp2)/(3000+ms1+mp1+mp2));
e2=isp2*g*log((3000+ms2+mp2)/(3000+ms2));
e3=mp1/(ms1+mp1);
e4=mp2/(3000+ms2+mp2);
eqn = [e1==deltav1, e2==deltav2, e3==0.9, e4==0.8].';

partial_mp1 = solve(eqn(1), mp1)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

partial_mp1 = 

eqn2 = subs(eqn(2:end), mp1, partial_mp1)

eqn2 = 

partial_mp2 = solve(eqn2(1), mp2)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

partial_mp2 = 

eqn3 = subs(eqn2(2:end), mp2, partial_mp2)

eqn3 = 

partial_ms1 = solve(eqn3(1), ms1)

partial_ms1 = 

eqn4 = subs(eqn3(2:end), ms1, partial_ms1)

eqn4 = 

ans = simplify(lhs(eqn4)) == rhs(eqn4)

ans = 

deltav1num = simplify(solve(ans,deltav1))

deltav1num = 

ms2num = solve(subs(eqn4,deltav1,deltav1num),ms2)

ms2num = 

0

ms1num = simplify(subs(partial_ms1,[ms2 deltav1],[ms2num deltav1num]))

ms1num = 

mp2num = simplify(subs(partial_mp2,[ms2 deltav1],[ms2num,deltav1num]))

mp2num = 

12000

mp1num = simplify(subs(partial_mp1,[ms1 ms2 mp2 deltav1],[ms1num ms2num mp2num deltav1num]))

mp1num = 

[Walter Roberson]

Torsten's version looks good.

[Torsten]

Seems that for eqn(1), the "solution" leads to a log(0/0) expression.

[Walter Roberson]

Maple says the solution is

deltav1 = -3136*ln(5)+9500

mp1 = 9*ms1

mp2 = -40*(exp(-32/29*ln(5)+4750/1421)*ms1+300*exp(-32/29*ln(5)+4750/1421)-ms1)/(4*exp(-32/29*ln(5)+4750/1421)-5)

ms2 = -10*(exp(-32/29*ln(5)+4750/1421)*ms1+1500*exp(-32/29*ln(5)+4750/1421)-ms1-1500)/(4*exp(-32/29*ln(5)+4750/1421)-5)

ms1 = anything

which does seem to satisfy the equations

Answer 2

[Andrew Nguyen]

Thank you both.