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After making a couple of comments on this StackExchange question, and pointing yet again to this article, a thought occurred to me.
I have been working on an Automatic Differentiation based ODE solver and equation analyzer, mentioned in this thread. Why not use it to solve equation (7) in the article, and plug in my answer to equation (8)? All I have to do is write a test client containing the appropriate equations ;)
Well, I had to do a bit of work to extract the equation solver results programmatically rather than just printing them out, but I did get it working! Here's what it looks like in the console (the ratio is of the proper times of the radial to circular paths):
A plot of the alpha function in the article is attached (function value is black, the rest are the first six derivatives). I am still in the process of testing for accuracy, but thought I'd post while I was motivated ;) If anyone wants to join in the fun, the software (which uses Python3 and matplotlib) is here.
I have been working on an Automatic Differentiation based ODE solver and equation analyzer, mentioned in this thread. Why not use it to solve equation (7) in the article, and plug in my answer to equation (8)? All I have to do is write a test client containing the appropriate equations ;)
Well, I had to do a bit of work to extract the equation solver results programmatically rather than just printing them out, but I did get it working! Here's what it looks like in the console (the ratio is of the proper times of the radial to circular paths):
Python:
$ ./grtwins.py 2 2 2 1001 0 1e9 1e9  ./plotMany.py 2 300 >/dev/null
taylor module loaded
series module loaded
playground module loaded
Newton's method
ResultType(count=4, sense='', mode='ROOT', x=1.5843306502838275, f=7.105427357601002e15, dx=1.0310205845716116e16)
(4.932330448527358, 1.3413587820012287)
n = 1
alpha = 1.5843306502838275
r1 = 4.932330448527358
r2 = 10.0
ratio = 1.3413587820012287
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