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

✍ Scribed by A.P. Ivanov; V.V. Samsonova

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 402 KB
• Volume: 64
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(00)00104-0

✦ Synopsis

A circular, restricted three-body problem is considered when a passively gravitating point also experiences the action of small resistive forces, acting 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 force to the force of gravitational attraction serves as the small parameter. Asymptotically stable periodic orbits are constructed. 'IWO Lyapunov families of periodic orbits, which exist in the neighbourhood of the libration points of the classical theory, are the generating families. Calculations were carried out for mass ratios corresponding to the Earth-Jupiter and Earth-Moon systems, with different values of the parameters characterizing the law of resistance.