Trajectory · Research
Your locked-in guess isn’t the answer — it’s the seed for a real Newton shooting solver. Tune a launch value, lock it, and watch the actual numerical method drive the boundary residual to machine precision (or diverge if your seed missed the basin). Every instance is generated from randomized physics — there’s no lookup table.
Classics
Earth–Moon L₁ Lyapunov
ẍ − 2ẏ = Ωₓ , ÿ + 2ẋ = Ω_y (rotating frame, μ = 0.0121)
The canonical Earth–Moon L₁ periodic orbit. Launch perpendicular from x₀ = 0.82 and lock a vy₀ — it seeds a real Newton shooting solver. Land in the basin and it converges to a closed orbit (vy₀ ≈ 0.1625); miss, and it diverges or finds a different family member.
Live readout
The knob swings on a timer — lock it (or hit Space) when the curve looks close. Locking seeds a real Newton shooting solver: it iterates the actual ODE and drives the residual toward zero, live. A good seed converges in a few steps; a bad one diverges or lands on a different orbit. That seed is the genuinely useful work — it’s what a continuation solver needs to start.