On the computation of the Lyapunov Characteristic Numbers of the planar restricted three-body problem

Details On the computation of the Lyapunov Characteristic Numbers of the planar restricted three-body problem On the computation of the Lyapunov Characteristic Numbers of the planar restricted three-body problem

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983acasn..24...58y&link_type=abstract

(Acta Astronomica Sinica, vol. 24, no. 1, 1983, p. 58-67) Chinese Astronomy and Astrophysics (ISSN 0275-1062), vol. 7, Sept. 198

Astronomy and Astrophysics

Astrophysics

Celestial Mechanics, Power Series, Three Body Problem, Equations Of Motion, Liapunov Functions, Variational Principles

Scientific paper

The use of the power series solution is investigated for the computation of the Lyapunov Characteristic Numbers (LCNs) of the regularized equations of the planar restricted three-body problem. It is determined that the use of the Sundman type of power series solution is more effective than the usual numerical methods, such as the RK78 and the linear multi-step methods, and significantly reduces the required computer time. In addition, it is shown that, in the limiting case where the infinitesimal body is indefinitely close to either of the finite bodies, all the LNCs should be zero.

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