The Hyperbolic, Eisenstein–Lattice, and FRLT Interpretation of the Figure‑Eight Choreography in the Three‑Body Problem

The figure‑eight three‑body choreography is reformulated using a complex shape parameter matching the hyperbolic structure of the figure‑eight knot complement. Its action becomes a hyperbolic geodesic functional, and the Eisenstein lattice’s unique fixed point serves as the FRLT pivot generating the orbit.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-18
DOI
https://doi.org/10.5281/zenodo.21986971
Primary Topic
Spacecraft Dynamics and Control
Type
article
Field-Weighted Citation Impact
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article

The Hyperbolic, Eisenstein–Lattice, and FRLT Interpretation of the Figure‑Eight Choreography in the Three‑Body Problem

Shin Tamaki
Zenodo (CERN European Organization for Nuclear Research)
Spacecraft Dynamics and Control
article

The Hyperbolic, Eisenstein–Lattice, and FRLT Interpretation of the Figure‑Eight Choreography in the Three‑Body Problem

Shin Tamaki
article en

Abstract

The figure‑eight three‑body choreography is reformulated using a complex shape parameter matching the hyperbolic structure of the figure‑eight knot complement. Its action becomes a hyperbolic geodesic functional, and the Eisenstein lattice’s unique fixed point serves as the FRLT pivot generating the orbit.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 6%
Spacecraft Dynamics and Control
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The Hyperbolic, Eisenstein–Lattice, and FRLT Interpretation of the Figure‑Eight Choreography in the Three‑Body Problem — Shin Tamaki · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS