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Fwd: I Need to Have These Equations Solved!
*To*: mathgroup at smc.vnet.net
*Subject*: [mg76733] Fwd: I Need to Have These Equations Solved!
*From*: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
*Date*: Sat, 26 May 2007 04:43:13 -0400 (EDT)
*References*: <f30vo2$mk0$1@smc.vnet.net> <465441A0.5080805@gmail.com>
[crossposted to MathGroup]
On 5/24/07, Andery <pskmaths at googlemail.com> wrote:
> Hi Jean,
>
> Thanks a lot for your help, I appreciate that for you so much. I tried the
> way you suggested but it takes a long time running without a result. But I
> will run it and leave it for a while and see.
>
> Now, I need you help to solve these three equations with repsect to r, s and
> theta.
>
> (1/4)*(-8*a*Î±*Î²*Sin[Î¸] - (4*l*m1*Î¼*(r*Cos[Î¸] - s*Sin[Î¸]))/(l^2 + r^2 + s^2 -
> 2*l*s*Cos[Î¸] - 2*l*r*Sin[Î¸])^(3/2) +
> (4*l*m1*Î¼*(r*Cos[Î¸] - s*Sin[Î¸]))/(l^2 + r^2 + s^2 + 2*l*s*Cos[Î¸] +
> 2*l*r*Sin[Î¸])^(3/2) + 2*(a - b)*Î±^2*Sin[2*Î¸]) = 0
>
> (-M)*r*Î±^2 + (m2*r*Î¼)/(r^2 + s^2)^(3/2) + (m1*Î¼*(r - l*Sin[Î¸]))/(l^2 +
> r^2 + s^2 - 2*l*s*Cos[Î¸] - 2*l*r*Sin[Î¸])^(3/2) +
> (m1*Î¼*(r + l*Sin[Î¸]))/(l^2 + r^2 + s^2 + 2*l*s*Cos[Î¸] +
> 2*l*r*Sin[Î¸])^(3/2) = 0
>
> Î¼*((m2*s)/(r^2 + s^2)^(3/2) + (m1*(s - l*Cos[Î¸]))/(l^2 + r^2 + s^2 -
> 2*l*s*Cos[Î¸] - 2*l*r*Sin[Î¸])^(3/2) +
> (m1*(s + l*Cos[Î¸]))/(l^2 + r^2 + s^2 + 2*l*s*Cos[Î¸] +
> 2*l*r*Sin[Î¸])^(3/2)) = 0
[snip]
Hi Andery,
Again, I strongly advise you to post the corrected message and your
request to MathGroup.
Second, the symbol for equality is still a double equal sign ==. A single
equal sign = is an immediate assignment (Set).
Finally, your second set of equations is also a system of
transcendentals equations and, in general,
such equations are difficult to solve analytically. You may want to
try Reduce, but I suspect that you will be more successful
by using some numerical approaches.
So, try to solve your system numerically and if you face any
difficulties, post a message to *MathGroup* with _a example of what
command you have tried and any results and warning/error messages_ .
Regards,
Jean-Marc
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