The sims_flanagan module contains our implementation of the low-thrust interplanetary trajectory optimization model first described in a paper by Sims and Flanagan in 1997 and later improved to include high-fidelity propagations and easy mesh refinement by the pykep development team. The key papers containing most details are:
Sims, Jon A., and Steve N. Flanagan. “Preliminary design of low-thrust interplanetary missions.” (1997).
Izzo, Dario. “pygmo and pykep: open source tools for massively parallel optimization in astrodynamics (the case of interplanetary trajectory optimization).” Proceed. Fifth International Conf. Astrodynam. Tools and Techniques, ICATT. 2012.
The list of classes and the detailed documentation follows.
Name |
Type |
Description |
|---|---|---|
class |
represents a nuclear electric propelled spacecraft |
|
class |
represent the spacecraft state (r,v,m) |
|
class |
represents one leg in the Sims-Flanagan model |
pykep.sims_flanagan.spacecraft(*args)¶Contains design parameters of a NEP spacecraft
__init__(*args)¶pykep.sims_flanagan.spacecraft(mass,thrust,isp)
mass: the spacecraft mass
thrust: the maximum thrust of the spacecraft propulsion system
isp: the specific impulse of the spacecarft propulsion system
Examples:
sc = sims_flanagan.spacecraft(4500,0.05,2500)
pykep.sims_flanagan.spacecraft(mass,thrust,isp)
mass: the spacecraft mass
thrust: the maximum thrust of the spacecraft propulsion system
isp: the specific impulse of the spacecarft propulsion system
Examples:
sc = sims_flanagan.spacecraft(4500,0.05,2500)
pykep.sims_flanagan.sc_state(*args)¶Represents the state of a spacecraft as position, velocity and mass
__init__(*args)¶pykep.sims_flanagan.sc_state(r,v,m)
r: triplet containing the position vector in cartesian coordiantes
v: triplet containing the velocity vector in cartesian coordiantes
m: mass
Examples:
x0 = sims_flanagan.sc_state((1,0,0),(0,1,0),1000)
pykep.sims_flanagan.sc_state(r,v,m)
r: triplet containing the position vector in cartesian coordiantes
v: triplet containing the velocity vector in cartesian coordiantes
m: mass
Examples:
x0 = sims_flanagan.sc_state((1,0,0),(0,1,0),1000)
set(*args)¶Sets the whole spacecraft state at once using a 7 dimensional tuple
Example:
x0.set((1,0,0,0,1,0,1000))
get(*args)¶Gets the whole spacecraft state at once putting it into a 7 dimensional tuple
Example:
state = x0.get()
pykep.sims_flanagan.leg(*args)¶represents one low-thrust trajectory leg in the sims-flanagan model
__init__(*args)¶pykep.sims_flanagan.leg(start,x0,throttles,end,xe,spacecraft,mu)
start: starting epoch
x0: starting sc_state
throttles: tuple containing the 3N cartesian components of the throttles
end: final epoch
xe: final sc_state
spacecarft: spacecraft
mu: central body gravity parameter
Example:
import pykep as pk start = pk.epoch(0)
end = pk.epoch(340)
earth = pk.planet.jpl_lp('earth')
mars = pk.planet.jpl_lp('mars')
sc = pk.sims_flanagan.spacecraft(4500,0.05,2500)
r,v = earth.eph(start)
x0 = pk.sims_flanagan.sc_state(r,v,sc.mass)
r,v = mars.eph(start)
xe = pk.sims_flanagan.sc_state(r, v ,sc.mass)
mu = pk.MU_SUN
l = pk.sims_flanagan.leg(start,x0,(1,0,0,0,0,1,0,0,0,0,1,0),end,xe,sc,mu)
pykep.sims_flanagan.leg(start,x0,throttles,end,xe,spacecraft,mu)
start: starting epoch
x0: starting sc_state
throttles: tuple containing the 3N cartesian components of the throttles
end: final epoch
xe: final sc_state
spacecarft: spacecraft
mu: central body gravity parameter
Example:
import pykep as pk start = pk.epoch(0)
end = pk.epoch(340)
earth = pk.planet.jpl_lp('earth')
mars = pk.planet.jpl_lp('mars')
sc = pk.sims_flanagan.spacecraft(4500,0.05,2500)
r,v = earth.eph(start)
x0 = pk.sims_flanagan.sc_state(r,v,sc.mass)
r,v = mars.eph(start)
xe = pk.sims_flanagan.sc_state(r, v ,sc.mass)
mu = pk.MU_SUN
l = pk.sims_flanagan.leg(start,x0,(1,0,0,0,0,1,0,0,0,0,1,0),end,xe,sc,mu)
set(*args)¶Sets leg’s data, leaving the spacecraft and the central body gravitational parameter unchanged
Example:
l.set(start,x0,(0,0,0,1,0,0,1,0,0,0,0,0),end,xe)
high_fidelity(*args)¶If True propagation is not impulsive, but continuous
Example:
l.high_fidelity = True
mismatch_constraints(*args)¶Returns a tuple containing the state mismatch of the leg x,y,z,vx,vy,vz,m (needs to be all zeros for the leg to be feasible)
Example:
ceq = l.mismatch_constraints()
throttles_constraints(*args)¶Returns a tuple containing the throttle magnitudes minus one
Example:
c = l.throttles_constraints()
set_mu(*args)¶Sets the leg central body gravitational parameter
Example:
l.set_mu(pykep.MU_SUN)
set_spacecraft(*args)¶Sets the leg spacecraft
Example:
sc = pykep.sims_flanagan.spacecraft(4500,0.05,2500)
l = pykep.sims_flanagan.leg() l.set_spacecraft(sc)
get_states()¶Returns the spacecraft states (t,r,v,m) at the leg grid points
Examples:
times,r,v,m = pykep.sims_flanagan.leg.get_states()