Question: Solve This! - Elliptic Integrals

Several weeks ago I submitted a request titled "Plot This! - Elliptic Integrals", which Dr. Robert Israel responded to with the following code which successfully plots the relationship of two variables, beta and k, over the range of interest. > with(plots); Digits := 15; > implicitplot(2*EllipticE(sin(beta), k)-EllipticF(sin(beta), k) = tan(beta)*sqrt(1-k^2*sin(beta)^2), k = 0 .. .99, beta = 3.5 .. 5.5, view = [0 .. 1, 3.5 .. 5.5]); However, the plot indicates that for the range of k=0..0.99, beta is approximately equal to 4.77 radians (273 degrees), whereas the paper that I am researching indicates a value of beta equal to 257 degrees 28 minutes. I have attached worksheet that includes the commands provided by Dr. Israel for information. a href=''>View on MapleNet or Download
View file details The objective at this point is to reproduce the curve shown in Figure 6, p. 694, in "A buckling problem of a circular ring.", Hsu Lo, et. al. According the paper, if one of three parameters is given, the other two can be solved can be determined from equations (15) and (16), and then the curve (viz., buckled shape) can be determined from (14). The paper is included for reference. I am requesting help in verifying the equation in the "implicitplot()" command listed above vs. the plot shown as Figure 5 in the paper. From that point, if someone could check my use of the fsolve command in the worksheet to solve for k and beta, given a value of N = 180. Download 4865_Lo_p691.pdf
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