Skip to main content

NEWTON-RAPSON METHOD FOR KEPLER’S ECCENTRICITY

##Constants and initializations
ecc=0.1; ## Eccentricity
M=24.851090; ## Mean anomaly(degrees)
Mr=M*pi/180; ## Mean anomaly (rads)
f=[]; ## The fundamental eqn we want to solve
## Kepler's Equation's zero function f(E)=E-esinE-M=0
fp=[]; ## 1st derivative of f(E). fp(E)=1+ecosE
Ed=[]; ## Eccentric anomaly(degrees)
Er=[]; ## Eccentric anomaly(rads)
Ed(1)=M+0.85*sign(sin(Mr))*ecc; ## The eccentric anomaly initial
## guess for Danby's method(degrees)
Er(1)=Ed(1)*pi/180; ## rads
for i=1:100
f(i)=Ed(i)-ecc*sin(Er(i))-M;
fp(i)=1+ecc*cos(Er(i));
Ed(i+1)=Ed(i)-f(i)/fp(i); ## The iteration for an updated eccentric anomaly E(i+1)
## based on a current value E(i) by Newton-Rapson Method
Er(i+1)=Ed(i+1)*pi/180;
endfor
save -text NEWTONRAPSON.dat
printf('We find E to be %f. This is the answer of Q1(a)\n',Ed(i+1));

Comments

Post a Comment

Popular posts from this blog

NEWTON-RAPSON METHOD-8th degree Legendre polynomial

## Newton-Rapson Method to the smallest non negative root
## of the 8th degree Legendre Polynomial
## P8(x)=(1/128)(6435x^8-12012x^6+6930x^4-1260x^2+35)
## where -1<=x<=1.
## for the smallest non negative root, we can ignore
## all the terms except the last two by truncated
## the function to be zero and find
## x=0.167 as the initial smallest non negative
## root.
##Constants and initializations
x=[]; ## Empty array for the iterated x roots
x(1)=0.16700000; ## Initial guess to begin the iteration for the
## smallest non-negative root.
L8=[]; ## Empty array for the Legendre polynomial
L8p=[]; ## Empty array for the derivative of the Legendre polynomial
for i=1:100
##The value of the function at x
L8(i)=(1/128)*(6435*x(i)^8-12012*x(i)^6+6930*x(i)^4-1260*x(i)^2+35);
##The value of the derivative of the function at x
L8p(i)=(1/128)*(6435*8*x(i)^7-12012*6*x(i)^5+6930*4*x(i)^3-1260*2*x(i));
x(i+1)=x(i)-L8(i)/L8p(i); ## the iteration
endfor
## For plot let's define a new variable…
Post a Comment
Read more

Second Harmonic Generation

gnuplot> set xrange [-180:180] gnuplot> set yrange [-180:180] gnuplot> set pm3d gnuplot> set hidden3d  gnuplot> set title 'SHG' gnuplot> splot sin(cos(x*pi/180))*sin(cos(x*pi/180))/(cos(x*pi/180)*cos(x*pi/180))*sin(cos(y*pi/180))*sin(cos(y*pi/180))/(cos(y*pi/180)*cos(y*pi/180)) title 'N=1
'
Post a Comment
Read more