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MathGroup Archive 2002

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Re: Why No Solution Using Solve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33914] Re: [mg33902] Why No Solution Using Solve?
  • From: Roberto Brambilla <rlbrambilla at cesi.it>
  • Date: Tue, 23 Apr 2002 07:13:25 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

At 00.57 22/04/02 -0400, you wrote:
>Why doesn't this give a solution?
>
>Solve[{
>m1 a1 == P1/ v1 - A1 Rho Cd (v1 + w)^2 /2 - m1 g Cr1 - m1 g S,
>m2 a2 == P2/ v2 - A2 Rho Cd (v2 + w)^2 /2 - m2 g Cr1 - m2 g S,
>m3 a3 == P3/ v3 - A3 Rho Cd (v3 + w)^2 /2 - m3 g Cr1 - m3 g S},
>{Cr1, S, w}
>]
>
>
>
>
Hi Tom,

collecting the last therms you have

Solve[{
    m1 a1 - P1/v1 == -A1 Rho Cd (v1 + w)^2/2 - m1 g( Cr1 + S),
    m2 a2 - P2/v2 == -A2 Rho Cd (v2 + w)^2/2 - m2 g (Cr1 + S),
    m3 a3 - P3/v3 == -A3 Rho Cd (v3 + w)^2/2 - m3 g (Cr1 + S)
    }, {Cr1, S, w}]

from which it is apparent that (Crl+S) are a sigle variable,
so the system is overdetermined.
Calling Crl+S=CrlS and eliminating an equation (for instance the third)
your system becomes

Solve[{
      m1 a1 - P1/v1 == -A1 Rho Cd (v1 + w)^2/2 - m1 g( Cr1S),
      m2 a2 - P2/v2 == -A2 Rho Cd (v2 + w)^2/2 - m2 g (Cr1S)
      }, {Cr1S, w}] // Simplify
 
Mathematica can solve this easily.
Bye, Roberto
Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.02.2125.5875
fax +39.02.2125.5492
rlbrambilla at cesi.it



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