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Solve system of four equations and rearrange it into four equations?

Ng Chong Lay, Student
Posted 7 years ago

enter image description here

I want to solve this four equations and rearrange it into four equation (g1,g2,J1,J2 in terms of a and h). I leave it to run around 12 hours but it show me nothing.

I tried simple equation with same format, it can be solved. I also tried to solve the equation separately but there are many possible answers due to it is nonlinear equation.

I am new in using Wolfram Mathematica. Can anyone help me with this? or at least explain to me why it run for a long time but cannot be solve. Thank you in advance.

EDITED: Below is the equation

Solve[{4*(a^2 + a*Sqrt[a^2 - 1]) - 2 == -(g1^2/(2*h*J1)) , a^2 == (J2^2*(1 - J1^2) + 2*J2*J1 - 1)/ (2*h*g2^2*J1), 
-(4*(a^2 + a*Sqrt[a^2 - 1]) - 1) == -((g2^2 - g2^2*J1^2 - 2*g1*g2 - g1^2*J2^2)/(2*h*g2^2*J1)) , J2 + J1*((g2*a)^2 - J2^2) == 0} , {J1, J2, g1, g2} ]
Attachments:
Qeustions.nb
POSTED BY: Ng Chong Lay
6 Replies
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It might simply be a difficult system to get into a "nice" form.

Numerically solving, once given numeric values for a and h, might not be so difficult though.
POSTED BY: Daniel Lichtblau
Bill Nelson
Bill Nelson
Posted 7 years ago
POSTED BY: Bill Nelson
Paul Cleary
Paul Cleary
Posted 7 years ago

More often than not you will need to put some limits on your variables, for example a>0, a<100, if you don't know what kind of results to expect I would start low with the limits. However, if you post your code so we can copy it we can be more specific with an answer.
POSTED BY: Paul Cleary

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The rules explain how to format your code properly. If you do not format code, it may become corrupted and useless to other members. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

enter image description here
POSTED BY: EDITORIAL BOARD

General rule: if you want people to try out your code, post it as code. Images cannot be copied-pasted as code.
POSTED BY: Daniel Lichtblau

Thank you for reminding. I edited my post.

POSTED BY: Ng Chong Lay
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