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MathGroup Archive 2007

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Re: I Need to Have These Equations Solved!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76584] Re: I Need to Have These Equations Solved!
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 24 May 2007 06:08:24 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <f30vo2$mk0$1@smc.vnet.net>

pskmaths at googlemail.com wrote:
> Hi everybody,
> 
> I have some long expresion equations and I have been struggling to get
> them solved! I need to solve these equations with respect to r, s, =CE=B8
> and =CF=95.
> 
> The solutions are subject to the follwoing:
> 
> 1=2E r>0
> 2=2E s>=0
> 3=2E 0<==CE=B8<=pi/2
> 4  0<==CF=95<pi
> 
> The equations are:
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> ------------
> 1=2E     (1/4)*(-8*a*=CE=B1*=CE=B2*Sin[=CE=B8] - (4*l*m1*=CE=BC*(r*Cos[=CE=
> =B8]*Cos[=CF=95] -
> s*Sin[=CE=B8]))/(l^2 + r^2 + s^2 - 2*l*s*Cos[=CE=B8] -
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) +
>     (4*l*m1*=CE=BC*(r*Cos[=CE=B8]*Cos[=CF=95] - s*Sin[=CE=B8]))/(l^2 + r^2 =
> + s^2 +
> 2*l*s*Cos[=CE=B8] + 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) + 2*(a - b)*=CE=B1=
> ^2*Sin[2*=CE=B8]) =
> 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> ------------
> 2=2E    (1/4)*((4*l*m1*r*=CE=BC*Sin[=CE=B8]*Sin[=CF=95])/(l^2 + r^2 + s^2 -
> 2*l*s*Cos[=CE=B8] - 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) -
>     (4*l*m1*r*=CE=BC*Sin[=CE=B8]*Sin[=CF=95])/(l^2 + r^2 + s^2 + 2*l*s*Cos[=
> =CE=B8] +
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2)) = 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> ------------
> 3=2E    (-M)*r*=CE=B1^2 + (m2*r*=CE=BC)/(r^2 + s^2)^(3/2) + (m1*=CE=BC*(r -
> l*Cos[=CF=95]*Sin[=CE=B8]))/(l^2 + r^2 + s^2 - 2*l*s*Cos[=CE=B8] -
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) +
>    (m1*=CE=BC*(r + l*Cos[=CF=95]*Sin[=CE=B8]))/(l^2 + r^2 + s^2 + 2*l*s*Cos=
> [=CE=B8] +
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) = 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> ------------
> 4=2E    =CE=BC*((m2*s)/(r^2 + s^2)^(3/2) + (m1*(s - l*Cos[=CE=B8]))/(l^2 + =
> r^2 +
> s^2 - 2*l*s*Cos[=CE=B8] - 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) +
>     (m1*(s + l*Cos[=CE=B8]))/(l^2 + r^2 + s^2 + 2*l*s*Cos[=CE=B8] +
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2)) = 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> ------------
> 
> 
> And also, I have another group of equations:
> 
> 
> 1=2E   =CE=B1*=CF=892*(-2*a*=CE=B2 + (a - b)*=CE=B1*Cos[=CE=B8])*Cos[=CF=95=
> ]^2*Sin[=CE=B8] +
> l*m1*r*=CE=BC*=CF=892*Cos[=CE=B8]*Cos[=CF=95]*
>     (-(1/(l^2 + r^2 + s^2 - 2*l*s*Cos[=CE=B8] - 2*l*r*Cos[=CF=95]*Sin[=CE=
> =B8])^(3/2))
> + 1/(l^2 + r^2 + s^2 + 2*l*s*Cos[=CE=B8] + 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(=
> 3/2)) +
>    l*m1*r*=CE=BC*=CF=891*(-(1/(l^2 + r^2 + s^2 - 2*l*s*Cos[=CE=B8] -
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2)) + 1/(l^2 + r^2 + s^2 + 2*l*s*Cos[=CE=
> =B8] +
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2))*
>     Sin[=CF=95] + =CF=892*Sin[=CE=B8]*(l*m1*s*=CE=BC*(1/(l^2 + r^2 + s^2 - =
> 2*l*s*Cos[=CE=B8] -
> 2*l*r*Cos[=CF=95]*Sin[=CE=B8])^(3/2) -
>        1/(l^2 + r^2 + s^2 + 2*l*s*Cos[=CE=B8] + 2*l*r*Cos[=CF=95]*Sin[=CE=
> =B8])^(3/2))
> + =CE=B1*(-2*a*=CE=B2 + (a - b)*=CE=B1*Cos[=CE=B8])*Sin[=CF=95]^2) = 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> -----------
> 2=2E    (-M)*r*=CE=B1^2 + m1*=CE=BC*(-((l*Cos[=CF=95]*Sin[=CE=B8])/(l^2 + r=
> ^2 + s^2 -
> 2*l*(s*Cos[=CE=B8] + r*Cos[=CF=95]*Sin[=CE=B8]))^(3/2)) +
>      (l*Cos[=CF=95]*Sin[=CE=B8])/(l^2 + r^2 + s^2 + 2*l*(s*Cos[=CE=B8] +
> r*Cos[=CF=95]*Sin[=CE=B8]))^(3/2)) = 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> -----------
> 3=2E   m1*=CE=BC*(-((l*Cos[=CE=B8])/(l^2 + r^2 + s^2 - 2*l*(s*Cos[=CE=B8] +
> r*Cos[=CF=95]*Sin[=CE=B8]))^(3/2)) +
>     (l*Cos[=CE=B8])/(l^2 + r^2 + s^2 + 2*l*(s*Cos[=CE=B8] +
> r*Cos[=CF=95]*Sin[=CE=B8]))^(3/2)) = 0
> ---------------------------------------------------------------------------=
> ---------------------------------------------------------------------------=
> -----------
> 
> 
> 
> Thanks a lot.
> 
> 

You post again your request to MathGroup, but this time using 
Mathematica InputForm for your expressions. Also, you should indicate 
what built-in functions and/or approach you have tried and their results.

How to use the *InputForm* when copying an expression from a
Mathematica notebook to an email client. Select the cell(s)
you want to include in your email, then within the *Cell* menu select
either *Convert To* or *Display As* and choose *InputForm*. Finally,
copy and paste as usual.

Regards,
Jean-Marc


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