The onset of chaotic motion in the restricted problem of three bodies

Details The onset of chaotic motion in the restricted problem of three bodies The onset of chaotic motion in the restricted problem of three bodies

Jul 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..409s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 3, p. 409-425.

Mathematics

Dynamical Systems

9

Chaos, Dynamical Systems, Three Body Problem, Jacobi Matrix Method, Liapunov Functions, Poincare Problem, Power Spectra

Scientific paper

A full characterization of a nonintegrable dynamical system requires an investigation into the chaotic properties of that system. One such system, the restricted problem of three bodies, has been studied for over two centuries, yet few studies have examined the chaotic nature of some of its trajectories. This paper examines and classifies the onset of chaotic motion in the restricted three-body problem through the use of Poincare surfaces of section, Liapunov characteristic numbers, power spectral density analysis, and a newly developed technique called numerical irreversibility. The chaotic motion is found to be intermittent and becomes first evident when the Jacobian constant is slightly higher than C2.

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