The Onset of Chaotic Motion in the Restricted Problem of Three Bodies
Abstract
A complete qualitative understanding of the solutions of a set of nonlinear differential equations requires an investigation of the chaotic properties of the system. The circular restricted problem of three bodies has a long and rich history of qualitative analysis, yet few studies have examined the possible existence of chaos in this problem. This study concentrates on the advent of chaos for widely different points in the phase space which correspond to closed Jacobian curves. Four methods are used to classify an orbit as chaotic. The first three techniques, Poincare surfaces of section, Liapunov characteristic numbers, and power spectral density analysis, are standard tools used in the study of nonlinear dynamics. A new method, called numerical irreversibility, is introduced and used in a comparison of the four techniques on a nonlinear map. With a criterion developed from this comparison, the character of chaos in the restricted problem of three bodies is examined and regions of chaotic motion in the phase space are identified. An upper bound on the Jacobian constant is set such that all orbits with Jacobian constants higher than that limit will be regular. Furthermore, applications of this analysis to space dynamics studies and planetary formation studies are investigated.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......100S
 Keywords:

 ORBITAL MECHANICS;
 Engineering: Aerospace, Physics: Astronomy and Astrophysics