Instability and Diffusion in the Elliptic Restricted Three-body Problem

Details Instability and Diffusion in the Elliptic Restricted Three-body Problem Instability and Diffusion in the Elliptic Restricted Three-body Problem

Jan 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998cemda..70...23l&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 70, Issue 1, p. 23-39 (1998).

Astronomy and Astrophysics

Astronomy

Resonant Orbit, Transversal Intersection, Resonant Jump, Diffusion, Instability

Scientific paper

The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic elliptic and hyperbolic elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's differential correction method. We find indications of stability for the elliptic elliptic resonance orbits because slightly perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance orbit of the hyperbolic elliptic type, we show numerically that its stable and unstable manifolds intersect transversally in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.

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