Code covered by the BSD License
- [fid, alt1, alt2, inc1, i...read orbital elements and simulation
- atan3 (a, b)
four quadrant inverse tangent
- brent (f, x1, x2, rtol)
solve for a single real root of a nonlinear equation
- ceqm1 (t, y)
first order form of Cowell's equations of orbital motion
- eci2mee(mu, reci, veci)
convert eci state vector to
- eci2orb1 (mu, r, v)
convert eci state vector to six classical orbital
- gast1 (jdate)
Greenwich apparent sidereal time
- gdate (jdate)
convert Julian date to Gregorian (calendar) date
- gravity (t, y)
first order equations of orbital motion
- hohmfunc (x)
inclination objective function
- j2eqm (t, y)
first order equations of orbital motion
- j4eqm(t, y)
first order equations of orbital motion
- julian (month, day, year)
Julian date
- mee2eci(mu, mee)
convert modified equinoctial orbital
- nc_event(t, y)
nodal crossing event function
- oeprint1(mu, oev, ittype)
print six classical orbital elements
- om_constants
astrodynamic and utility constants
- orb2eci(mu, oev)
convert classical orbital elements to eci state vector
- readgm(fname)
read gravity model data file
- rkf78 (deq, neq, ti, tf, ...solve first order system of differential equations
- svprint(r, v)
print position and velocity vectors and magnitudes
- tpbvp(x)
two point boundary value objective function and
- twobody2 (mu, tau, ri, vi)solve the two body initial value problem
- ueci2angles(reci, veci, u...convect eci unit vector to rtn angles
- hohmann.m
- phohmann.m
-
View all files
from
The Gravity Perturbed Hohmann Transfer
by David Eagle
MATLAB script for solving the Hohmann transfer problem perturbed by non-spherical Earth gravity.
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| brent (f, x1, x2, rtol)
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function [xroot, froot] = brent (f, x1, x2, rtol)
% solve for a single real root of a nonlinear equation
% Brent's method
% input
% f = objective function coded as y = f(x)
% x1 = lower bound of search interval
% x2 = upper bound of search interval
% rtol = algorithm convergence criterion
% output
% xroot = real root of f(x) = 0
% froot = function value at f(x) = 0
% Orbital Mechanics with MATLAB
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
global iter;
% machine epsilon
eps = 2.23e-16;
e = 0;
a = x1;
b = x2;
fa = feval(f, a);
fb = feval(f, b);
fc = fb;
for iter = 1:1:50
if (fb * fc > 0)
c = a;
fc = fa;
d = b - a;
e = d;
end
if (abs(fc) < abs(fb))
a = b;
b = c;
c = a;
fa = fb;
fb = fc;
fc = fa;
end
tol1 = 2 * eps * abs(b) + 0.5 * rtol;
xm = 0.5 * (c - b);
if (abs(xm) <= tol1 || fb == 0)
break;
end
if (abs(e) >= tol1 && abs(fa) > abs(fb))
s = fb / fa;
if (a == c)
p = 2 * xm * s;
q = 1 - s;
else
q = fa / fc;
r = fb / fc;
p = s * (2 * xm * q * (q - r) - (b - a) * (r - 1));
q = (q - 1) * (r - 1) * (s - 1);
end
if (p > 0)
q = -q;
end
p = abs(p);
min = abs(e * q);
tmp = 3 * xm * q - abs(tol1 * q);
if (min < tmp)
min = tmp;
end
if (2 * p < min)
e = d;
d = p / q;
else
d = xm;
e = d;
end
else
d = xm;
e = d;
end
a = b;
fa = fb;
if (abs(d) > tol1)
b = b + d;
else
b = b + sign(xm) * tol1;
end
fb = feval(f, b);
end
xroot = b;
froot = fb;
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