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Solve system of 3 equations using "Solve"

Liyaqat Nazir
Posted 5 years ago
Attachments:
Systemofeqns.nb
POSTED BY: Liyaqat Nazir
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Liyaqat Nazir
Liyaqat Nazir
Posted 5 years ago

@Aaron Crenshaw Thank you for your valuable suggestion. Sir, you are right. These solutions do not satisfy the three equations. The calculated values cannot probably be wrong because the research article is by a renowned author and has served the foundation for many other papers. It might be possible that these three calculated equations might have some error which I am not able to figure out. I think this because up to values of C1 and C2 I have cross-checked the Wolfram Mathematica results as well as those given in the research article using hand calculations. After that point hand calculations became complex and not doable. Moreover, Vcc is the supply voltage and cannot be Zero. I have also posted a reduced form of mathematica notebook of same problem in stack exchange forum Simplified form. For more clarity, I have also attached the Research article I am trying to solve. I will be highly thankful if you could help me in debugging the error.

Attachments:
Paper.pdf
POSTED BY: Liyaqat Nazir
0 0
0 0
Posted 5 years ago

Greetings Liyaqat,

Before we work on solving this problem, have you checked that the answer provided is correct? I tried to verify it and assuming everything else is correct, I find that 

Vcc == 0 && -1. C L \[Omega] + C^2 L^2 \[Omega]^3 != 0

This means that Vcc must be zero when you say it is assumed to be constant. Is this an expected result?

I attached some the edits I made to produce this result.

qsol = 1.607;
phisol = -41.614;
VRsol = 0.9253*Vcc;

eqn1 = eq4 /. {q -> qsol, phi -> phisol, VR -> VRsol} // FullSimplify
eqn2 = eq5b /. {q -> qsol, phi -> phisol, VR -> VRsol} // 
  FullSimplify
eqn3 = eq6c /. {q -> qsol, phi -> phisol, VR -> VRsol} // FullSimplify


Reduce[{eqn1, eqn2, eqn3}]
Attachments:
Systemofeqns.nb
POSTED BY: 0 0
Liyaqat Nazir
Liyaqat Nazir
Posted 5 years ago

I have posted a simpler form of this post in matematica.stackexchange forum the link for that is Stackexchange

POSTED BY: Liyaqat Nazir

You can make the system algebraic using TrigExpand and converting the cosines and sines to new variables e.g. Cos[phi]->cphi,... Also add the defining relations e.g. cphi^2+sphi^2==1. This will give an algebraic system in the new variables that might or might not be tractable, but at least it can be handled algorithmically (that is, a method is implemented that covers this class).
POSTED BY: Daniel Lichtblau
Liyaqat Nazir
Liyaqat Nazir
Posted 5 years ago

Thank you Daniel for your reply. I had some formatting issues in the post. I have corrected the post now in proper format for its clarity. I hope the question is clear now.
POSTED BY: Liyaqat Nazir
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