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Solve equation with First and Second type of Elliptical Integral?

studygroups 2000
Posted 11 years ago

Hi,

I am trying to solve elliptical equation that contain First and Second kind of elliptical. I did not get any result. I tried below steps

k = Simplify[[[4*R*r]/[[f - Y]^2 + [r + R]^2]]^1/2, Assumptions -> {r = 0.05, R = 0.3, f = 0.1, Y = 0.8}]
A = EllipticK[k]
B = EllipticE[k]
N = [R*r]^1/2/[2*Pi*k][[2 - k^2]*A - [2*B]] // FullSimplify

Thanks
POSTED BY: studygroups 2000
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Hello,

Thank you so much for all your help!
POSTED BY: studygroups 2000
POSTED BY: Gerard Kopcsay

Rules are only applied using RelpaceAll[] for each individual expression, so the substitutions are not done globally. Also, you did not assign the result of the first expression to k. I think this is what you are trying to do.

k = ((4*R*r)/((f - Y)^2 + (r + R)^2))^1/2 /. {r -> 0.05, R -> 0.3, 
    f -> 0.1, Y -> 0.8};
A[k_] := EllipticK[k];
B[k_] := EllipticE[k];
(R*r)^1/2/(2*Pi*k) ((2 - k^2)*A[k] - 2*B[k]) /. {r -> 0.05, R -> 0.3}
POSTED BY: Gerard Kopcsay

Hello,

Really I appreciate that. It is work!

 k = ((4*R*r)/((f - Y)^2 + (r + R)^2))^1/2 /. {r -> 0.05, R -> 0.3,  f -> 0.1, Y -> 0.8};
 A[k_] := EllipticK[k];
 B[k_] := EllipticE[k];
 J = (R*r)^1/2/(2*Pi*k) ((2 - k^2)*A[k] - 2*B[k]) /. {r -> 0.05, R -> 0.3, Y -> 0.8} // Simplify

Output

 -0.0756162 + 0.0486827 1.55561[0.0489796]
POSTED BY: studygroups 2000

Generally, rules are used with Mathematica to substitute numerical values into expressions containing symbols. Something like the following should work with the expression that you tried.

((4*R*r)/((f - Y)^2 + (r + R)^2))^1/2 /. {r -> 0.05, R -> 0.3, 
  f -> 0.1, Y -> 0.8}
POSTED BY: Gerard Kopcsay

Hello,

Thank you so much for your reply. Please I still got the result as function of E(K). How I can get it without E(k). In addition, In original equation I have k^2. How I can assign the result from first equation to be k for second, third, and forth equations?

((4*R*r)/((f - Y)^2 + (r + R)^2))^1/2 /. {r -> 0.05, R -> 0.3, f -> 0.1, Y -> 0.8}
A[k_] := EllipticK[k];
B[k_] := EllipticE[k];
(R*r)^1/2/(2*Pi*k) ((2 - k^2)*A[k] - 2*B[k]) // FullSimplify

Output

(r R (2 EllipticE[5] + 23 EllipticE[(4 r R)/((r + R)^2 + (-2 + Y)^2)][5]))/(20 \[Pi])
POSTED BY: studygroups 2000

Hello,

Thank you so much for your reply. Please I have the value of r,R,f, and Y. and I define k as

k = Simplify[((4*R*r)/((f - Y)^2 + (r + R)^2))^1/2, Assumptions -> {r = 0.05, R = 0.3, f = 0.1, Y = 0.8}]

I want to get out of K(k) and E(k) in final result.

Thanks
POSTED BY: studygroups 2000
POSTED BY: S M Blinder
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