Astronomy5 papers
Dynamics of unstable main belt asteroids
IŽ
Ivana Milić Žitnik
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intermediate
Short Lyapunov time: a method for identifying confined chaos
O. C. Winter et al. (2010)
- Published
- Nov 1, 2010
- Journal
- Astronomy & Astrophysics · Vol. 523
- DOI
- 10.1051/0004-6361/200912734
At a Glance
A simple “radial Lyapunov” diagnostic separates short-time chaos that escapes from chaos that stays radially confined.
Summary
Short Lyapunov times usually signal rapid orbital diffusion, but some bodies remain radially bounded despite being strongly chaotic (“confined/stable chaos”). This paper introduces an easy add-on to standard Lyapunov exponent calculations that estimates how much of the divergence occurs specifically in the radial direction by measuring separations in a rotating frame aligned with the orbit’s radius. Applied to asteroids perturbed by Jupiter and to Saturn F-ring moonlets perturbed by Prometheus/Pandora, the method cleanly distinguishes escapers (radial contribution comparable to total) from confined chaos (radial contribution orders of magnitude smaller). The implication is a practical screening tool: short Lyapunov time alone is insufficient, but “radial LCE” helps predict whether chaos will translate into large semimajor-axis/radius changes.
Method Snapshot
Compute the maximal Lyapunov exponent via nearby-orbit divergence while simultaneously projecting the separation onto a rotating radial frame to estimate a radial-only exponent.
Background
Background in dynamical systems/chaos (Lyapunov exponents) and basic celestial mechanics (restricted three-body/ring-satellite perturbations).