hiten 0.2.8

HITEN - Computational Toolkit for the Circular Restricted Three-Body Problem

HITEN - Computational Toolkit for the Circular Restricted Three-Body Problem

Overview

HITEN is a research-oriented Python library that provides an extensible implementation of high-order analytical and numerical techniques for the circular restricted three-body problem (CR3BP).

Examples

1. Parameterisation of periodic orbits and their invariant manifolds

   The toolkit constructs periodic solutions such as halo orbits and computes their stable and unstable manifolds.

   from hiten import System
   
   system = System.from_bodies("earth", "moon")
   l1 = system.get_libration_point(1)
   
   orbit = l1.create_orbit("halo", amplitude_z=0.2, zenith="southern")
   orbit.correct(max_attempts=25)
   orbit.propagate(steps=1000)
   
   manifold = orbit.manifold(stable=True, direction="positive")
   manifold.compute()
   manifold.plot()
   

   

   Figure 1 - Stable manifold of an Earth-Moon (L_1) halo orbit.

   Knowing the dynamics of the center manifold, initial conditions for vertical orbits can be computed and associated manifolds created. These reveal natural transport channels that can be exploited for low-energy mission design.

   from hiten import System, VerticalOrbit
   
   system = System.from_bodies("earth", "moon")
   l1 = system.get_libration_point(1)
   
   cm = l1.get_center_manifold(max_degree=10)
   cm.compute()
   
   initial_state = cm.ic(poincare_point=[0.0, 0.0], energy=0.6, section_coord="q3")
   
   orbit = VerticalOrbit(l1, initial_state=initial_state)
   orbit.correct(max_attempts=100)
   orbit.propagate(steps=1000)
   
   manifold = orbit.manifold(stable=True, direction="positive")
   manifold.compute()
   manifold.plot()
   

   

   Figure 2 - Stable manifold of an Earth-Moon (L_1) vertical orbit.

2. Generating families of periodic orbits

   The toolkit can generate families of periodic orbits by continuation.

   from hiten import System
   from hiten.algorithms import StateParameter
   
    system = System.from_bodies("earth", "moon")
    l1 = system.get_libration_point(1)
   
    seed = l1.create_orbit('lyapunov', amplitude_x= 1e-3)
    seed.correct(max_attempts=25)
   
    target_amp = 1e-2 # grow A_x from 0.001 to 0.01 (relative amplitude)
    current_amp = seed.amplitude
    num_orbits = 10
   
    # Step in amplitude space (predictor still tweaks X component)
    step = (target_amp - current_amp) / (num_orbits - 1)
   
    engine = StateParameter(
        initial_orbit=seed,
        state=(S.X),     # underlying coordinate that gets nudged
        amplitude=True,  # but the continuation parameter is A_x
        target=(current_amp, target_amp),
        step=step,
        corrector_kwargs=dict(max_attempts=50, tol=1e-13),
        max_orbits=num_orbits,
    )
    engine.run()
   
    family = OrbitFamily.from_engine(engine)
    family.propagate()
    family.plot()
   

   

   Figure 3 - Family of Earth-Moon (L_1) Lyapunov orbits.

3. Generating Poincaré maps

   The toolkit can generate Poincaré maps for the centre manifold over various sections.

   from hiten import System
   
   system = System.from_bodies("earth", "moon")
   l1 = system.get_libration_point(1)
   
   cm = l1.get_center_manifold(max_degree=12)
   cm.compute()
   
   pm = cm.poincare_map(energy=0.7, section_coord="q2", n_seeds=50, n_iter=100, seed_strategy="axis_aligned")
   pm.compute()
   pm.plot()
   

   

   Figure 4 - Poincaré map of the centre manifold of the Earth-Moon (L_1) libration point using the (q_2=0) section.

4. Generating invariant tori

   Hiten can generate invariant tori for periodic orbits.

   from hiten import System
   from hiten.algorithms import InvariantTori
   
    system = System.from_bodies("earth", "moon")
    l1 = system.get_libration_point(1)
   
    orbit = l1.create_orbit('halo', amplitude_z=0.3, zenith='southern')
    orbit.correct(max_attempts=25)
    orbit.propagate(steps=1000)
   
    torus = InvariantTori(orbit)
    torus.compute(scheme='linear', epsilon=1e-2, n_theta1=256, n_theta2=256)
    torus.plot()
   

   

   Figure 5 - Invariant torus of an Earth-Moon (L_1) quasi-halo orbit.