Syntax

Intro

The syntax of this tool can be divided into two different applications. The first one deals with single halo orbit computation by directly utilizing the Orbit class. The second application is about halo orbit families and therefore based on the HaloFamily class. In this chapter, every method of these classes and their individual syntax is presented.

Orbit Class

An orbit can be instantiated by:

testOrbit = Orbit(x0, fixedValue, mu, jacobi, stability, NRHO)

Keyword	Description	Data Type	Mandatory	Default
x0	Initial guess of halo orbit	Float array	YES	-
fixedValue	Value will be fixed during iterative corrections scheme	String: {"x", "z"}	YES	-
mu	Mass ratio	Float	YES	-
jacobi	Jacobi constant	Float	NO	None
stability	Stability index	Float	NO	None
NRHO	NRHO classification	Bool	NO	False

As already explained in Program Structure, the Orbit class includes four methods:

Method	Description	Input Parameters	Mandatory	Default
getNearestNRHO()	Searches for closest NRHO	-	-	-
getJacobi()	Calculates Jacobi constant	-	-	-
getStability	Calculates stability index	-	-	-
plot(background, haloFamily)	Plots figure of orbit	String: background: {"on", "off"} haloFamily: {"both", "northern", "southern}	NO	background="off", haloFamily="both"

Example

For the sake of clarity, the initial guess needed for both a single halo orbit and a halo orbit family as well as constants like the mass ratio should be defined before instantiating an object:

mFirstPrimary = 5.97237e+24  # Earth
mSecondPrimary = 7.342e+22  # Moon
mu = mSecondPrimary / (mSecondPrimary + mFirstPrimary)
x0 = np.array([1.10156010, 0, -0.19840472, 0, -0.21676273, 0])

Orbit = Orbit(x0, "x", mu)

Orbit.plot()  # top left figure
Orbit.plot(background="on")  # top right figure
Orbit.plot(background="on", haloFamily="northern")  # bottom left figure
Orbit.plot(background="on", haloFamily="southern")  # bottom right figure

OrbitFamily Class

A family of halo orbit can be instantiated by three different ways:

testFamily = OrbitFamily(x0, orbitDistance, mu, familyData) 

testFamily_L1 = L1Family(x0, orbitDistance, mu, familyData) 

testFamily_L2 = L2Family(x0, orbitDistance, mu, familyData)

Keyword	Description	Data Type	Mandatory	Default
x0	Initial guess of halo orbit	Float array	YES	-
orbitDistance	Desired distance between orbits	Float	YES	-
mu	Mass ratio	Float	YES	-
familyData	Include initial guess and period of orbits	Float array	NO	None

These classes include three methods. When using L1Family() or L2Family(), the parameter lagrangian is NOT used.

Method	Description	Input Parameters	Mandatory	Default
getHaloFamily(lagrangian)	Uses Natural Parameter Continuation to find family of halo orbits	String: {"L1", "L2"}	YES	-
getNRHOFamily(lagrangian)	Uses Natural Parameter Continuation and Pseudo-Arclength Continuation to find family of NRHO	String: {"L1", "L2"}	YES	-
plot(lagrangian, background, haloFamily)	Plots figure of orbit	String: background: {"on", "off"} haloFamily: {"both", "northern", "southern}	lagrangian: YES	background="off", haloFamily="both"

Example

mFirstPrimary = 5.97237e+24  # Earth
mSecondPrimary = 7.342e+22  # Moon
mu = mSecondPrimary / (mSecondPrimary + mFirstPrimary)
l1 = np.array([0.8233901862, 0, -0.0029876370, 0, 0.1264751431, 0])
l2 = np.array([1.1808881373, 0, -0.0032736457, 0, -0.1559184478, 0])

family1 = OrbitFamily(l1, 0.002, mu)
family1.plot("L1")  # left figure

family2 = L2Family(l2, 0.002, mu)
family2.plot()  # right figure