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