Help a noob implement MATLAB for a math iteration

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James
James 2013-10-8
评论： Jan 2013-10-13
Alright guys I'm new to Matlab and have no idea how to use it. I've read the manual but I still don't understand. I need to implement Kepler's problem iteration.
equation 1: 0.69=E-0.82sinE where E is in radians. A random E will be plugged in by the user, and the MATLAB program has to iterate until 0.69 is achieved.
There's a formula for the E iteration values.
equation 2: E(i+1)=Ei+(0.69-Mi)/(1-0.82cosEi) This reads the E subscript i+1 value equals the E subscript i value ......etc. The Mi is equivalent to equation 1, where M=0.69. So Mi would just be what Ei plugged during the iteration.
Example: I choose Ei=0.5 and plug it into my iterative MATLAB function. Then equation 1 becomes M=0.5-0.82sin0.5. Hence Mi=0.10687. Then solve equation 2 for E(i+1). Get E(i+1)=2.5796. Then this becomes the next E value, and the process repeats itself UNTIL 0.69-Mi goes near to 0. I need a convergence tolerance of 10^-7, whatever that means.
I apologize for my poor explanation of the math problem. Fortunately the textbook is online: http://www.fgg.uni-lj.si/~/mkuhar/Zalozba/Fundamentals_of_Astrodynamics-Bate_Mueller&White-1971.pdf
Go to pages 220-222 (the book pages) section 4.6.4. Equation 1 is 4.2-6, and equation 2 is 4.6-40.
Do I use a if function?
Thanks.
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Duke
Duke 2013-10-11
One of the big things that’s wrong with this forum is being think they are above everyone else because they know a broken tool better than other people (The amount of down time MatLab caused me when it crashed is astronomical). I found Matt reply as him being a jerk and belittling the poster. There are a few other people that are sarcastic all the time as well. I have no idea what the poster said, but after the comment Matt left I'd be upset as well.
Jan
Jan 2013-10-13
Sorry, Duke. I've removed by contributions to this discussion, because I assume, it is not of public interest. Unfortunately this steals the context of your comment.
I suggest not to take the messages of others personally in a forum.

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sixwwwwww
sixwwwwww 2013-10-10
编辑：sixwwwwww 2013-10-10
Dear James here is the code according to your problem description:
Ei = input('Enter initial value E[rad]: ');
diff = 1;
iteration_count = 0;
while diff >= 1e-7
Mi = Ei - 0.82 * sin(Ei);
diff = abs(0.69 - Mi);
E_next = Ei + (0.69 - Mi) / (1 - 0.82 * cos (Ei));
Ei = E_next;
iteration_count = iteration_count + 1;
end
disp(strcat('Number of iterations: ', num2str(iteration_count)))
disp(strcat('Final value of Mi:', num2str(Mi)))
disp(strcat('Final value of Ei:', num2str(Ei)))
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Jan
Jan 2013-10-10
Or slightly simplified:
Ei = input('Enter initial value E[rad]: ');
iteration_count = 0;
Mi = Inf;
while abs(0.69 - Mi) >= 1e-7
Mi = Ei - 0.82 * sin(Ei);
Ei = Ei + (0.69 - Mi) / (1 - 0.82 * cos (Ei));
iteration_count = iteration_count + 1;
end
fprintf('Number of iterations: %d\n', iteration_count)
fprintf('Final value of Mi: %g\n', Mi)
fprintf('Final value of Ei: %g\n', Ei)
I did not check the algorithm.

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