On the Sitnikov problem

Details On the Sitnikov problem On the Sitnikov problem

Sep 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..49..285l&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 49, no. 3, 1990, p. 285-302. NNSFC-supported research.

Statistics

Computation

19

Equations Of Motion, Hyperbolic Differential Equations, Stellar Motions, Three Body Problem, Celestial Mechanics, Center Of Mass, Computational Astrophysics, Elliptical Orbits, Entropy, Transformations (Mathematics)

Scientific paper

The simple restricted three-body problem known as the Sitnikov problem is investigated analytically by means of conformal mapping. The formulation of the governing differential equations is outlined; the fundamental mapping and some modified versions are derived and compared with the original equations; the existence of a hyperbolic invariant set is proved; the chaotic regions of the mapping are characterized using Liapunov exponents; and the global stochasticity of the mapping as a dynamical system is measured in terms of the Kustaanheimo-Steifel entropy. Good agreement is demonstrated between the analytical determinations of chaotic regions and the results of numerical computations.

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