hiten 0.3.1

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).

Installation

HITEN is published on PyPI. A recent Python version (3.9+) is required.

py -m pip install hiten

Optional dev tools (formatting, linting, tests):

py -m pip install "hiten[dev]"

Quickstart

Compute a halo orbit around Earth–Moon L1 and plot a branch of its stable manifold:

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()

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(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, OrbitFamily
   from hiten.algorithms import StateParameter
   from hiten.algorithms.utils.types import SynodicState
   
   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=SynodicState.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 arbitrary sections. For example, the centre manifold of the Earth-Moon (L_1) libration point:

   from hiten import System
   
   system = System.from_bodies("earth", "moon")
   l1 = system.get_libration_point(1)
   
   cm = l1.get_center_manifold(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.

   Or the synodic section of a vertical orbit manifold:

   from hiten import System, VerticalOrbit
   from hiten.algorithms import SynodicMap, SynodicMapConfig
   
   system = System.from_bodies("earth", "moon")
   l_point = system.get_libration_point(1)
   
   cm = l_point.get_center_manifold(degree=6)
   cm.compute()
   
   ic_seed = cm.ic([0.0, 0.0], 0.6, "q3") # Good initial guess from CM
   
   orbit = VerticalOrbit(l_point, initial_state=ic_seed)
   orbit.correct(max_attempts=100, finite_difference=True)
   orbit.propagate(steps=1000)
   
   manifold = orbit.manifold(stable=True, direction="positive")
   manifold.compute(step=0.005)
   manifold.plot()
   
   section_cfg = SynodicMapConfig(
      section_axis="y",
      section_offset=0.0,
      plane_coords=("x", "z"),
      interp_kind="cubic",
      segment_refine=30,
      newton_max_iter=10,
   )
   synodic_map = SynodicMap(section_cfg)
   synodic_map.from_manifold(manifold)
   synodic_map.plot()
   

   

   Figure 5 - Synodic map of the stable manifold of an Earth-Moon (L_1) vertical orbit.

4. Detecting heteroclinic connections

   The toolkit can detect heteroclinic connections between two manifolds.

   from hiten.algorithms.connections import Connection, SearchConfig
   from hiten.algorithms.poincare import SynodicMapConfig
   from hiten.system import System
   
   system = System.from_bodies("earth", "moon")
   mu = system.mu
   
   l1 = system.get_libration_point(1)
   l2 = system.get_libration_point(2)
   
   halo_l1 = l1.create_orbit('halo', amplitude_z=0.5, zenith='southern')
   halo_l1.correct()
   halo_l1.propagate()
   
   halo_l2 = l2.create_orbit('halo', amplitude_z=0.3663368, zenith='northern')
   halo_l2.correct()
   halo_l2.propagate()
   
   manifold_l1 = halo_l1.manifold(stable=True, direction='positive')
   manifold_l1.compute(integration_fraction=0.9, step=0.005)
   
   manifold_l2 = halo_l2.manifold(stable=False, direction='negative')
   manifold_l2.compute(integration_fraction=1.0, step=0.005)
   
   section_cfg = SynodicMapConfig(
      section_axis="x",
      section_offset=1 - mu,
      plane_coords=("y", "z"),
      interp_kind="cubic",
      segment_refine=30,
      tol_on_surface=1e-9,
      dedup_time_tol=1e-9,
      dedup_point_tol=1e-9,
      max_hits_per_traj=None,
      n_workers=None,
   )
   
   conn = Connection(
      section=section_cfg,
      direction=None,
      search_cfg=SearchConfig(delta_v_tol=1, ballistic_tol=1e-8, eps2d=1e-3),
   )
   
   conn.solve(manifold_l1, manifold_l2)
   print(conn)
   conn.plot(dark_mode=True)
   

   

   Figure 6 - Heteroclinic connection between the stable manifold of an Earth-Moon (L_1) halo orbit and the unstable manifold of an Earth-Moon (L_2) halo orbit.

5. 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 7 - Invariant torus of an Earth-Moon (L_1) quasi-halo orbit.

Run the examples

Example scripts are in the examples directory. From the project root:

py -m pip install -e .
python examples\periodic_orbits.py
python examples\orbit_family.py
python examples\synodic_map.py
python examples\heteroclinic_connection.py

Contributing

Issues and pull requests are welcome. For local development:

py -m pip install -e .[dev]
python -m pytest -q

License

This project is licensed under the terms of the MIT License. See LICENSE.