Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation

Details Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation

Sep 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005ap%26ss.299..129p&link_type=abstract

Astrophysics and Space Science, Volume 299, Issue 2, pp.129-148

Astronomy and Astrophysics

Astrophysics

6

Restricted Three-Body Problem, Angular Velocity, Long- And Short-Period Families, Trojan Manifold

Scientific paper

We study numerically the asymmetric periodic orbits which emanate from the triangular equilibrium points of the restricted three-body problem under the assumption that the angular velocity ω varies and for the Sun Jupiter mass distribution. The symmetric periodic orbits emanating from the collinear Lagrangian point L 3, which are related to them, are also examined. The analytic determination of the initial conditions of the long- and short-period Trojan families around the equilibrium points, is given. The corresponding families were examined, for a combination of the mass ratio and the angular velocity (case of equal eigenfrequencies), and also for the critical value ω = 2 sqrt2 , at which the triangular equilibria disappear by coalescing with the inner collinear equilibrium point L 1. We also compute the horizontal and the vertical stability of these families for the angular velocity parameter ω under consideration. Series of horizontal critical periodic orbits of the short-Trojan families with the angular velocity ω and the mass ratio μ as parameters, are given.

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