Astronomy5 papers
Dynamics of unstable main belt asteroids
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Ivana Milić Žitnik
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On the reliability of computation of maximum Lyapunov Characteristic Exponents for asteroids
Zoran Kneževic & Slobodan Ninkovic (2004)
- Published
- Aug 1, 2004
- Journal
- Proceedings of the International Astronomical Union · Vol. 2004 · No. IAUC197
- DOI
- 10.1017/S1743921304008646
At a Glance
Tests show maximum Lyapunov exponents from finite asteroid integrations are usually reliable, but can fail when dynamics shift.
Summary
This paper asks whether catalogued maximum Lyapunov characteristic exponents (LCEs) for asteroids—computed from finite-time numerical integrations—can be trusted as indicators of chaos. Using large-scale Orbit9/OrbFit integrations, the authors compare LCE estimates from forward vs. backward propagation and from different integration lengths (2, 10, 100 Myr), finding agreement for most objects (≈81.5% in ±1 Myr tests; ≈63.5% in a problem-biased 2 vs. 10 Myr subset). The main failure mode is not numerical noise per se but real time-variability: some asteroids switch dynamical regimes, producing slope changes in γ(t) and integration-span–dependent LCE estimates. Practically, the results support using catalog LCEs for broad classification (regular vs. chaotic; weak/moderate vs. strong chaos) while flagging a minority where LCEs are intrinsically unstable over time.
Method Snapshot
Compute maximum LCEs via variational-equation tracking during N-body orbit integrations and assess robustness by forward/backward and multi-timespan comparisons.
Background
Basic celestial mechanics and nonlinear dynamics/chaos concepts (Lyapunov exponents, numerical orbit integration).