Using a while loop/iterative process to derive a function

Question

Ryan Bowman 2019-3-21

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回答： Krishna Kumar 2019-3-21

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I am trying to use Kepler's equation to derive a f where f is a function of E. Here is the problem statement.

My code does not seem to spit out the right answer. I don't believe I'm really deriving the function. Here is my code:

clc;    
close all;  
clear;
format long e
% Problem 1
nt = 1.047197551 %equal to pi/3 in radians
ep = 0.3
Ei = 0;
iteration_count = 0;
Mi = inf;
while abs(1.047197551-Mi) >= 1e-7
    Mi = Ei-0.3*sin(Ei);
    Ei = Ei+(1.047197551-Mi)/(1-0.3*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)

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Answer 1

Krishna Kumar 2019-3-21

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The code yields final value of Ei, and you are essentially using Newton's method to solve the eqn. Do you want the code to print del_E rather? or do you find an error in final value of Ei. Probably you can double check the answer with nonlinear solvers like fsolve in matlab.