| _version_ | 1866901746994905088 |
|---|---|
| author | Lombardo, James |
| author_facet | Lombardo, James |
| contents | <p>Abstract</p> <p>We present a first-principles derivation of chaotic tumbling in Saturn's moon Hyperion using the</p> <p>Timeless Dynamics (TD) configuration-space framework. Starting from the topology factor</p> <p>eta0</p> <p>= 1.4780 and the S3 phase-transition structure derived in TD v15.1, we construct a complete</p> <p>chain to the chaos condition for any asymmetric rigid body in a gravitational gradient. The key steps</p> <p>are: (1) a corrected operator mapping that places Euler coupling terms as Christoffel symbols of the</p> <p>SO(3) metric rather than phase-gradient terms; (2) an exact mode-coupling integral kappa12</p> <p>= 1/16</p> <p>on S3 giving a renormalization-group flow equation for the effective coupling etaR(epsilon); (3) an ICI</p> <p>flow coefficient beta = 1/4 derived from the S3 mode projection, yielding the chaos condition</p> <p>lambda/omega > etaR,eff</p> <p>- 4 = 0.235. A quaternion-based integrator of the full three-dimensional</p> <p>Euler-tidal system produces Lyapunov times of 12.7-23.9 days across six initial conditions, clearing</p> <p>the derived threshold by a factor of five in every case. The observed Lyapunov time of ~36 days lies</p> <p>outside this range by 2.2x; the gap is located in initial-condition sampling and mass-distribution</p> <p>uncertainty and does not affect the sign of the prediction. The topology factor eta0</p> <p>= 1.4780 is</p> <p>load-bearing throughout: it sets the stability margin and therefore the chaos threshold.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19555824 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Chaotic Rotation of Hyperion from Configuration-Space Geometry Lombardo, James <p>Abstract</p> <p>We present a first-principles derivation of chaotic tumbling in Saturn's moon Hyperion using the</p> <p>Timeless Dynamics (TD) configuration-space framework. Starting from the topology factor</p> <p>eta0</p> <p>= 1.4780 and the S3 phase-transition structure derived in TD v15.1, we construct a complete</p> <p>chain to the chaos condition for any asymmetric rigid body in a gravitational gradient. The key steps</p> <p>are: (1) a corrected operator mapping that places Euler coupling terms as Christoffel symbols of the</p> <p>SO(3) metric rather than phase-gradient terms; (2) an exact mode-coupling integral kappa12</p> <p>= 1/16</p> <p>on S3 giving a renormalization-group flow equation for the effective coupling etaR(epsilon); (3) an ICI</p> <p>flow coefficient beta = 1/4 derived from the S3 mode projection, yielding the chaos condition</p> <p>lambda/omega > etaR,eff</p> <p>- 4 = 0.235. A quaternion-based integrator of the full three-dimensional</p> <p>Euler-tidal system produces Lyapunov times of 12.7-23.9 days across six initial conditions, clearing</p> <p>the derived threshold by a factor of five in every case. The observed Lyapunov time of ~36 days lies</p> <p>outside this range by 2.2x; the gap is located in initial-condition sampling and mass-distribution</p> <p>uncertainty and does not affect the sign of the prediction. The topology factor eta0</p> <p>= 1.4780 is</p> <p>load-bearing throughout: it sets the stability margin and therefore the chaos threshold.</p> |
| title | Chaotic Rotation of Hyperion from Configuration-Space Geometry |
| url | https://doi.org/10.5281/zenodo.19555824 |