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MathGroup Archive 2007

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I Need to Have These Equations Solved!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76456] I Need to Have These Equations Solved!
  • From: pskmaths at googlemail.com
  • Date: Wed, 23 May 2007 04:58:47 -0400 (EDT)

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.



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