A simplification in the calculation of the characteristic exponents of the plane circular model of three bodies

Details A simplification in the calculation of the characteristic exponents of the plane circular model of three bodies A simplification in the calculation of the characteristic exponents of the plane circular model of three bodies

Mar 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..46...79k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 46, no. 1, 1989, p. 79-84.

Statistics

Computation

Computational Astrophysics, Jacobi Integral, Three Body Problem, Boundary Value Problems, Equations Of Motion

Scientific paper

It is shown that, to evaluate the two nontrivial characteristic exponents of the plane circular model of three bodies, we need only to integrate the variational equation for two displacements, rather than four, as is usually done. The two displacements should be chosen to lie in the constant Jacobi manifold and to be initially perpendicular to the given periodic motion. This simplification is applicable to both general orbits (integration over one whole period) and symmetric orbits (integration over one half period).

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