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MathGroup Archive 2002

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Re: Solving problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32387] Re: Solving problem
  • From: Erk Jensen <Erk.Jensen at cern.ch>
  • Date: Fri, 18 Jan 2002 00:17:32 -0500 (EST)
  • References: <a25uuu$dk4$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Nicolas Le Roux wrote:
> 
> I have to solve a system of 4 equations with 4 variables. The problem is
> that one of a variable is a born(?) of an integrale and so Mathematica
> could not know whether or not the integrale is convergent. If you could
> help me to solve this system, it would really help me.
> You'll find the worksheet at www.via.ecp.fr/~genji/test.nb
> 
> Thank you
> 
> --
> Genji
> "La femme ne voit jamais ce qu'on fait pour elle, elle ne voit que ce
> qu'on ne fait pas."
> Georges Courteline

I'm not a guru, but why do you use "set delayed"? If you evaluate the integral
BEFORE you try and solve the equations, you don't get the problem you encounter.
However, I don't believe that you can solve the equations all analytically. What
I did is

\!\(eqns = 
    Simplify[{\@\(h\^2 - e\^2\) - a*e\^2 - b\ e - c == 0, 
        2\ a\ e + b + \(2\ e\)\/\@\(h\^2 - e\^2\) == 0, 
        a\ d\^2 + b\ d + c == 0, 
        L == \[Integral]\_e\%d\(\@\( 1 + b\^2 + 4\ a\ x\ b\  + \ 
                      4\ a\^2\ x\^2\)\) \[DifferentialD]x + 
            h\ \((\[Pi]\/2 - ArcCos[e\/h])\)}]\)

and then solved the 1st 3 equations for {a,b,c}, like

Solve[eqns[[{1, 2, 3}]], {a, b, c}] // Simplify

and insert the result into the forth like

eq4=eqns[[4]] /. %

Now you can plot the RHS - L versus e. This doesn't solve your real problem
however, the function doesn't seem to be well-behaved there ...

Good luck,
     -erk-


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