Effect of a perturbing potential on the stability of periodic solutions of the first kind

Details Effect of a perturbing potential on the stability of periodic solutions of the first kind Effect of a perturbing potential on the stability of periodic solutions of the first kind

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cha%26a...7..177j&link_type=abstract

Chinese Astronomy and Astrophysics, Volume 7, Issue 3, p. 177-186.

Astronomy and Astrophysics

Astrophysics

1

Scientific paper

We first use polar coordinates to discuss the effect of a perturbing potential on the existence of periodic solutions of the first kind. We then use the KAM theory to discuss the effect on their stability. Assuming the perturbing potential to have the form ? as usually found in practice, we show that as long as the angular velocity of the small body in the rotating frame is not equal to ? Poincaré's periodic orbits of the first kind analytically continued from circular orbits are stable. The above potential covers the cases where the larger primary is oblate or has a ring.

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