e2m2e — Earth to Moon, Moon to Earth

e2m2e (Earth to Moon, Moon to Earth) is a Python library based on the Circular Restricted Three-Body Problem (CR3BP), focused on designing and analyzing cislunar space transfer trajectories.

Core Features

CR3BP System Modeling: Supports Earth-Moon, Sun-Earth, Sun-Jupiter systems
Multiple Orbit Types: DRO, ARO, RO, Halo, Lyapunov, Lissajous, Butterfly, Dragonfly
Orbit Design Algorithms: Differential correction, natural continuation, pseudo-arclength continuation, stability analysis
Transfer Trajectory Search: Grid search, NLP optimization, impulsive transfer design
Visualization Tools: 2D/3D orbit plotting, Jacobi constant plots, stability analysis plots

Supported Orbit Types

Orbit Type	Description
DRO	Distant Retrograde Orbit
RO	Resonant Orbit (3:2, 4:3, etc.)
ARO	Axial Resonant Orbit
Halo	Halo orbit (periodic orbit)
Lyapunov	Lyapunov orbit (planar periodic)
Lissajous	Lissajous orbit (quasi-periodic)
Butterfly	Butterfly orbit (symmetric about xy-plane)
Dragonfly	Dragonfly orbit (multiple symmetries)

Installation

pip install e2m2e

Development dependencies:

pip install e2m2e[dev]

Example Usage

import e2m2e
from e2m2e.core import CR3BP_System, Orbit
from e2m2e.algorithms import DifferentialCorrection, Continuation

# 1. Create Earth-Moon system and compute libration points
system = CR3BP_System(mu=0.01215, primary="earth", secondary="moon")
system.compute_libration_points()
system.info()

# 2. Create dynamics object and seed orbit
dynamics = e2m2e.core.dynamics.CR3BP_Dynamics(system=system)
x0 = 0.79188556619742
vy0 = 0.53682
initial_state = [x0, 0.0, 0.0, 0.0, vy0, 0.0]
seed_orbit = Orbit(states=[initial_state], times=[0])
seed_orbit.period = 3.472526005624708

# 3. Differential correction to generate DRO orbit
corrector = DifferentialCorrection(dynamic=dynamics)
corrector.setup_2D_symmetric_x_fixed_x0(x0=x0)
seed_dro = corrector.iterate_correction(initial_guess=seed_orbit)

# 4. Natural continuation to generate orbit family
continuation = Continuation(corrector=corrector)
family = continuation.natural_continuation(
    seed_orbit=seed_dro,
    param_range=(0.14, 0.9),
    step_size=0.005,
)

# 5. Visualization
from e2m2e.visualization import OrbitVisualizer
viz = OrbitVisualizer(system)
viz.plot_2d_projection(seed_dro, plane='xy', color='blue')
viz.plot_primary_bodies()
viz.plot_libration_points()
viz.show()

Project Structure

e2m2e/
├── core/                 # Core modules
│   ├── system.py         # CR3BP system definition
│   ├── dynamics.py       # Dynamics model
│   ├── orbit.py          # Orbit data structure
│   └── coordinate.py     # Coordinate transformation
├── algorithms/           # Algorithm modules
│   ├── differential_correction.py  # Differential correction
│   ├── continuation.py            # Orbit continuation
│   └── stability.py              # Stability analysis
├── transfer/            # Transfer trajectory design
│   ├── transfer_search.py         # DRO transfer search
│   ├── transfer_optimization.py   # NLP optimization
│   └── transfer_base.py           # Base class
└── visualization/       # Visualization
    └── plotting.py     # Plotting tools