The existence of a chaotic region due to the overlap of secular resonances nu5 and nu6

Details The existence of a chaotic region due to the overlap of secular resonances nu5 and nu6 The existence of a chaotic region due to the overlap of secular resonances nu5 and nu6

Jun 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..49..177s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 49, no. 2, 1990, p. 177-196.

Statistics

Computation

4

Asteroid Belts, Chaos, Orbit Perturbation, Orbital Resonances (Celestial Mechanics), Secular Variations, Computational Astrophysics, Gravitational Constant, Hamiltonian Functions

Scientific paper

A nonlinear theory of secular resonances is developed. Both terms corresponding to secular resonances nu5 and nu6 are taken into account in the Hamiltonian. The simple overlap criterion is applied and the condition for the overlap of these resonances is found. The overlap criterion yields a critical value of parameter p depending on the semi-major axis a of the asteroid. For p greater than the critical value, a resonance overlap occurs and chaotic motion has to be expected. A mapping is presented for the fast calculation of the trajectories. The results are illustrated by level curves in surfaces of the section method.

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