The construction of periodic orbits close to triangular libration points for the three-body problem in a resistive medium

A circular, restricted three-body problem is considered when a passively gr avitating point also experiences the action of small resistive forces, acti ng in the opposite direction to the absolute velocity vector. The nature of the loss of stability of the triangular libration points is studied using the Poincare method in which the ratio of the magnitude of the resistive fo rce to the force of gravitational attraction serves as the small parameter. Asymptotically stable periodic orbits are constructed. Two Lyapunov famili es of periodic orbits, which exist in the neighbourhood of the libration po ints of the classical theory, are the generating families. Calculations wer e carried out for mass ratios corresponding to the Earth-Jupiter and Earth- Moon systems, with different values of the parameters characterizing the la w of resistance. (C) 2001 Elsevier Science Ltd. All rights reserved.