def set_coe(self, coe, units = None, rv = True):
if units != None:
from unit_conversions import converter
coe[2] = converter(coe[2], units, 'Radians')
coe[3] = converter(coe[3], units, 'Radians')
coe[4] = converter(coe[4], units, 'Radians')
coe[5] = converter(coe[5], units, 'Radians')
# reset coe
self.sma = coe[0]
self.e = coe[1]
self.i = coe[2]
self.RAAN = coe[3]
self.AOP = coe[4]
self.f = coe[5]
self.coe = [self.sma, self.e, self.i, self.RAAN, \
self.AOP, self.f]
# reset r, v
if rv:
from auxiliary import coe2rv
self.r, self.v = coe2rv(self.coe, self.Mu)
# recalculate additional useful orbital parameters
#+ E: eccentricy anomaly
#+ M: mean anomaly
#+ T: orbital period
#+ n: mean motion
from auxiliary import f2E, E2M, orbitalperiod
from math import pi
self.E = f2E(self.e, self.f)
self.M = E2M(self.e, self.E)
self.T = orbitalperiod(self.Mu, self.sma)
self.n = 2.0*pi / self.T
def set_sma(self, sma):
self.sma = sma
# reset sma in coe list
self.coe[0] = sma
# reset the r and v vectors
from auxiliary import coe2rv
self.r, self.v = coe2rv(self.coe, self.Mu)
# reset the orbital period
from auxiliary import orbitalperiod
self.T = orbitalperiod(self.Mu, self.sma)
# reset the mean motion
from math import pi
self.n = 2.0*pi / self.T
def prussing_conway(
ic1,
ic2,
mu,
TransferTime=0,
FindTimeParabolic=False,
FindMinEnergy=False,
FindlambertArc=False,
Retrograde=False,
NonDimUnits=True,
ScaleOutput=True,
iLimit=500,
tol=1e-2,
):
"""
prussing_conway()
Future Work
1.) Need to eliminate v1, v2 input arguments / 2014_05_18
2.) lambert should be able to use minimum time for
TransferTime without having to call lambert() twice
3.) Should separate lambert functions into a separate module,
which should eliminate r,v being set to 3d vectors from 2d
by rv2coe() call
4.) scipy calls appear to be working fine, should eliminate
all the junk code floating around and cleanup
5.) Shouldn't be rescaling if not using NonDimUnits
6.) Need Spatial Capability!!!
"""
""" DEBUG_SCIPY """
DEBUG_SCIPY = True
# import statements
from math import acos, asin, sin, pi, cos, sqrt
from numpy import array
from numpy.linalg import norm
from auxiliary import rv2coe, hohmann, orbitalperiod
# initialze output dictionary
out = {
"a": -1,
"res": -1,
"iter": 0,
"alpha": -1,
"beta": -1,
"tp": -1,
"tm": -1,
"v1": 0,
"v2": 0,
"DU": -1,
"TU": -1,
"MU": -1,
"theta": -1,
}
# select lambert arc computation if neither
# parabolic time nor min. energy selected
if not FindTimeParabolic and not FindMinEnergy:
FindlambertArc = True
# initializations
r1 = ic1[0:2]
r2 = ic2[0:2]
v1 = ic1[2:4]
v2 = ic2[2:4]
# convert r, v to coe
oe1 = rv2coe(r1, v1, mu)
oe2 = rv2coe(r2, v2, mu)
# convert to array type
r1 = array(r1[0:2])
r2 = array(r2[0:2])
v1 = array(v1[0:2])
v2 = array(v2[0:2])
# nondim units
G = 6.67384 * 1e-20 # (km^3/kg/s^2)
DU = oe1[0]
MU = mu / G
TU = sqrt(1 / (G * MU / DU ** 3))
if NonDimUnits:
mu = 1
# scaling
oe1[0] = oe1[0] / DU
oe2[0] = oe2[0] / DU
r1 = r1 / DU
r2 = r2 / DU
v1 = v1 * TU / DU
v2 = v2 * TU / DU
TransferTime = TransferTime / TU
# chord and semiperimeter
chord = norm(r1 - r2)
semip = (norm(r1) + norm(r2) + chord) / 2
# rotation of r1, 90 degrees
temp = array([-r1[1], r1[0]])
# find angle between r1 and r2
theta = acos(r1.dot(r2) / (norm(r1) * norm(r2)))
theta2 = acos(temp.dot(r2) / (norm(r1) * norm(r2)))
if theta2 >= pi / 2:
theta = 2 * pi - theta
# update out entry
out["theta"] = theta
# sign of sin(theta)
if sin(theta) < 0:
sgn = -1
if sin(theta) > 0:
sgn = 1
if sin(theta) == 0:
sgn = 0
# parabolic transfer time
if FindTimeParabolic or FindlambertArc:
tp = time_parabolic(semip, chord, mu, sgn)
out["tp"] = tp
if FindTimeParabolic:
return out
# calculate the minimum energy transfer time (elliptic case)
if FindMinEnergy or FindlambertArc:
tm = time_minenergy(semip, chord, mu, theta)
out["tm"] = tm
if FindMinEnergy:
return out
# let the user know if they selected an infeasbile
# + transfer time
if TransferTime < tp:
print(
"lambert: The transfer time (%.2f) is too short "
"for an Elliptic Orbit (< %.2f) --> Return" % (TransferTime, tp)
)
return out
# calculate semi-major axis, alpha, and beta
# scale tol if nondimunits == False
if not NonDimUnits:
tol = tol * DU
""" DEBUGGING for scipy.optimize 2014_05_18 """
if not DEBUG_SCIPY:
# initialize
res = 10 * tol
a = semip / 2 # oe1[0]
ainc = a * 1e-3
dir = 1
dx = ainc
damp = 10
i = 1
# while-loop unitl tolerance is met
while res > tol:
# save old
if i == 2:
temp = res
if i > 2:
res0 = temp
temp = res
# flip the direction of ainc if necessary
if i > 2 and res > res0:
dir = -1 * dir
# calculate damping needed
if i > 2 and res < res0:
slope = (res - res0) / ainc
if res > 0:
dx = -res / slope
if dx / ainc < damp:
ainc = ainc / 2
# update a
a = a + dir * ainc
# calculate residual
res = lamberteq(a, mu, TransferTime, semip, chord, tm, theta)
# if limit reached -> break
if i > iLimit:
break
# update i
i += 1
if DEBUG_SCIPY:
""" DEBUGGING for scipy.optimize 2014_05_18 """
from scipy.optimize import minimize
a = semip / 2
bnds = ((a, None),)
res = minimize(lamberteq, array(a), (mu, TransferTime, semip, chord, tm, theta), bounds=bnds, method="L-BFGS-B")
""" DEBUGGING for scipy.optimize 2014_05_18 """
# print res
a = res.x
i = 0
# alpha and beta are the rectilinear equivalent of
# eccentric anomaly for transfer orbit
alpha = 2 * asin(sqrt(semip / (2.0 * a)))
beta = 2 * asin(sqrt((semip - chord) / (2.0 * a)))
# perform necessary corrections
if TransferTime > tm:
alpha = 2 * pi - alpha
if theta >= pi and theta < 2 * pi:
beta = -beta
# switches for retrograde orbits.
# will need post-shooting method to adjust
if Retrograde == True:
beta = -beta
# compute delta-vs
# use hohmann if beta ~0 or ~180 degrees
# else
# use default calculations for v1 and v2
u1 = r1 / norm(r1)
u2 = r2 / norm(r2)
uc = (r2 - r1) / norm(r2 - r1)
# if abs(pi - (alpha - beta)) < 1E-4 and oe1[1] < 1E-2 and oe2[1] < 1E-2:
if abs(beta % pi) < 1e-4:
dv1, dv2 = hohmann(mu, oe1[0], oe2[0])
v1 = v1 + dv1 * v1 / norm(v1)
v2 = v2 + dv2 * v2 / norm(v2)
else:
cota = cos(alpha / 2) / sin(alpha / 2)
cotb = cos(beta / 2) / sin(beta / 2)
A = sqrt(mu / (4 * a)) * cota
B = sqrt(mu / (4 * a)) * cotb
v1 = (B + A) * uc + (B - A) * u1
v2 = (B + A) * uc - (B - A) * u2
# compute semilatus rectum for output
p = 4 * a * (semip - norm(r1)) * (semip - norm(r2)) * (sin((alpha + beta) / 2) ** 2) / (chord ** 2)
# compute orbital elements, output ecc and true anomaly
oef = rv2coe(r1, v1, mu)
f = oef[5]
# if retrograde, mod() true anomaly (i.e. flip i pi)
if abs(oef[2] - pi) < 1e-3:
f = 2 * pi - oef[5]
psi = 2 * pi - f
ev = [cos(psi) * u1[0] - sin(psi) * u1[1], sin(psi) * u1[0] + cos(psi) * u1[1]]
# position of the vacant focus
pf = [-2 * a * oef[1] * ev[0], -2 * a * oef[1] * ev[1]]
# compile output
out["a"] = a
out["e"] = oef[1]
out["ev"] = ev
out["f"] = oef[5]
out["T"] = orbitalperiod(mu, a)
out["pf"] = pf
""" DEBUGGING scipy.optimize 2014_05_18 """
if DEBUG_SCIPY:
out["res"] = res.fun
if not DEBUG_SCIPY:
out["res"] = res
out["iter"] = i - 1
out["alpha"] = alpha
out["beta"] = beta
out["time"] = TransferTime
out["v1"] = v1
out["v2"] = v2
out["DU"] = DU
out["TU"] = TU
out["MU"] = MU
# scale ouput if needed
if ScaleOutput:
out["a"] = out["a"] * DU
out["T"] = out["T"] * TU
out["tp"] = out["tp"] * TU
out["tm"] = out["tm"] * TU
out["v1"] = out["v1"] * DU / TU
out["v2"] = out["v2"] * DU / TU
return out
def set_parameters(self, body, altitude = 400.0):
import solarsystem_objects_parameters as ss
# setup parameters for the requested body if available
# first see if the user is requesting the 'Earth' or
#+ if the body is not on the given list, then default
#+ to the 'Earth'
if body == 'earth' or body not in ss.list:
self.name = 'earth'
# default classical orbital elements is
#+ earth about sun
self.sma = ss.earth['SemiMajor']
self.e = ss.earth['Eccentricity']
self.i = ss.earth['Inclination']
self.RAAN = 0.0
self.AOP = 0.0
self.f = 0.0
# epoch (Julian Date), default January 3rd 2014
#+ which is roughly when the Earth is at periapsis
self.epoch = 2456660.500000 * 86400.0
# mass and mu of the body
self.mass = ss.earth['Mass']
self.mu = ss.earth['Mu']
# radius of body
self.radius = ss.earth['Radius']
# set the gravitational constant of 'self'
#+ central body
self.Mu = ss.sun['Mu']
if body == 'sun':
self.name = 'sun'
# default classical orbital elements is
#+ earth about sun
self.sma = 0.0
self.e = 0.0
self.i = 0.0
self.RAAN = 0.0
self.AOP = 0.0
self.f = 0.0
# epoch (Julian Date), default January 3rd 2014
#+ which is roughly when the Earth is at periapsis
self.epoch = 2456660.500000 * 86400.0
# mass and mu of the body
self.mass = ss.sun['Mass']
self.mu = ss.sun['Mu']
# radius of body
self.radius = ss.sun['Radius']
# set the gravitational constant of 'self'
#+ central body
self.Mu = ss.sun['Mu']
if body == 'moon':
self.name = 'moon'
# default classical orbital elements is
#+ earth about sun
self.sma = ss.moon['SemiMajor']
self.e = ss.moon['Eccentricity']
self.i = ss.moon['Inclination']
self.RAAN = 0.0
self.AOP = 0.0
self.f = 0.0
# epoch (Julian Date), default January 3rd 2014
#+ which is roughly when the Earth is at periapsis
self.epoch = 2456660.500000 * 86400.0
# mass and mu of the body
self.mass = ss.moon['Mass']
self.mu = ss.moon['Mu']
# radius of body
self.radius = ss.moon['Radius']
# set the gravitational constant of 'self'
#+ central body
self.Mu = ss.earth['Mu']
if body == 'mars':
self.name = 'mars'
# default classical orbital elements is
#+ earth about sun
self.sma = ss.mars['SemiMajor']
self.e = ss.mars['Eccentricity']
self.i = ss.mars['Inclination']
self.RAAN = 0.0
self.AOP = 0.0
self.f = 0.0
# epoch (Julian Date), default January 3rd 2014
#+ which is roughly when the Earth is at periapsis
self.epoch = 2456660.500000 * 86400.0
# mass and mu of the body
self.mass = ss.mars['Mass']
self.mu = ss.mars['Mu']
# radius of body
self.radius = ss.mars['Radius']
# set the gravitational constant of 'self'
#+ central body
self.Mu = ss.sun['Mu']
if body == 'LEO':
self.name = 'leo_spacecraft'
# default classical orbital elements is
#+ spacecraft about earth
from math import pi
self.sma = ss.earth['Radius'] + altitude
self.e = 0.0
self.i = 28.5 * pi / 180.0
self.RAAN = 0.0
self.AOP = 0.0
self.f = 0.0
# epoch (Julian Date), default January 3rd 2014
#+ which is roughly when the Earth is at periapsis
self.epoch = 2456660.500000 * 86400.0
# mass and mu of the body
self.mass = 1000.0
self.mu = 0.0
# set the gravitational constant of 'self'
#+ central body
self.Mu = ss.earth['Mu']
# place the classical orbital elements into an array
self.coe = [self.sma, self.e, self.i, self.RAAN, \
self.AOP, self.f]
# calculate the r, v vectors for 'self'
#+ based on the classical orbital elements 'coe'
from auxiliary import coe2rv
self.r, self.v = coe2rv(self.coe, self.Mu)
# calculate additional useful orbital parameters
#+ E: eccentricy anomaly
#+ M: mean anomaly
#+ T: orbital period
#+ n: mean motion
from auxiliary import f2E, E2M, orbitalperiod
from math import pi
self.E = f2E(self.e, self.f)
self.M = E2M(self.e, self.E)
self.T = orbitalperiod(self.Mu, self.sma)
self.n = 2.0*pi / self.T
