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

Author: Papadakis, K.

Source: Astrophysics and Space Science, Volume 299, Number 2, September 2005 , pp. 129-148(20)

Publisher: Springer

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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  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  = 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  under consideration. Series of horizontal–critical periodic orbits of the short-Trojan families with the angular velocity  and the mass ratio  as parameters, are given.

Keywords: Trojan manifold; angular velocity; long- and short-period families; restricted three-body problem

Document Type: Research Article


Affiliations: Department of Engineering Sciences, Division of Applied Mathematics and Mechanics, University of Patras, GR-26504 Patras, Greece, Email:

Publication date: September 1, 2005

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