Lambert Jl

Lambert.jl

Julia library for solving Lambert's problem (two-position, time-of-flight orbital boundary value problem). Repo: HAMMERHEAD-Space/Lambert.jl

Architecture

Solver Hierarchy

AbstractLambertSolver <: SciMLBase.AbstractSciMLAlgorithm
├── GoodingSolver      # Gooding 1990 - robust, accurate
├── IzzoSolver         # Izzo 2015 - very fast
├── ValladoSolver      # Vallado 2013 - guaranteed convergence (bisection)
├── AroraSolver        # Arora 2013 - fast cosine transformation
├── BattinSolver       # Battin 1984 - handles 180° singularity
├── GaussSolver        # Gauss 1809 - historical, limited accuracy
└── AvanziniSolver     # Avanzini 2008 - eccentricity-based, single rev

Problem Types

AbstractAstroProblem <: SciMLBase.AbstractSciMLProblem
└── LambertProblem     # (μ, r1, r2, tof)

LambertSolution        # (v1, v2, numiter, retcode)
LambertIterator        # Stateful iterator for solve!

Source Layout

src/
  Lambert.jl            # Module, imports SciMLBase.solve/remake/init/solve!
  lambert_problem.jl    # LambertProblem, LambertSolution, LambertIterator
  utils.jl              # Stumpff functions, geometry, normalization, Lagrange coefficients
  porkchop.jl           # PorkchopGrid, porkchop_grid() with EnsembleProblem
  {solver_name}_solver.jl  # One file per solver algorithm
ext/
  LambertPlotsExt.jl    # Weak dep for porkchop plot visualization

Key Patterns

SciML Interface

# Object-oriented (recommended)
prob = LambertProblem(μ, r1, r2, tof)
sol = solve(prob, GoodingSolver())
# sol.v1, sol.v2, sol.numiter, sol.retcode

# Remake for parameter sweeps
prob2 = remake(prob; tof=new_tof)

Direct Function Call

v1, v2, numiter, converged = gooding1990(μ, r1, r2, tof; M=0, prograde=true)

Solver Configuration

Solvers use @with_kw for keyword defaults:

@with_kw struct GoodingSolver <: AbstractLambertSolver
    M::Int = 0             # Number of complete revolutions
    prograde::Bool = true  # Prograde transfer
    low_path::Bool = true  # Low-energy path (multi-rev)
    maxiter::Int = 35
    atol::Float64 = 1e-5
    rtol::Float64 = 1e-7
end

Porkchop Grids

grid = porkchop_grid(μ, r1_func, r2_func, dep_dates, arr_dates, solver;
    ensemble_method=EnsembleThreads())

Uses SciMLBase.EnsembleProblem for parallel grid evaluation.

Return Codes

:SUCCESS, :MAXIMUM_ITERATIONS, :COLLINEAR_VECTORS, :NEGATIVE_TOF

AstroCoords Integration

LambertProblem accepts any AstroCoord for positions -- auto-converts to Cartesian.

Heuristic Algorithm Selection

select_lambert_algorithm() chooses optimal solver based on transfer angle and revolution count.

Adding a New Solver

1. Create src/newsolver_solver.jl
2. Define @with_kw struct NewSolver <: AbstractLambertSolver with config fields
3. Implement SciMLBase.solve(prob::LambertProblem, alg::NewSolver)
4. Implement direct function newsolver(μ, r1, r2, tof; kwargs...)
5. Add to ALL_SOLVERS test constant
6. Test against reference solutions (Vallado, Curtis, Battin textbooks)
7. Add @check_allocs test (if allocation-free)

Dependencies

• AstroCoords 0.3, SciMLBase 2.67, Parameters 0.12
• Roots 2.2 (root-finding for some solvers)
• StaticArraysCore 1.4
• Weak dep: Plots 1.40 (porkchop visualization extension)