The 3D restricted three-body problem under angular velocity variation

Department of Engineering Sciences, Division of Applied Mathematics and Mechanics, University of Patras, 26504 Patras, Greece e-mail: K.Papadakis@des.upatras.gr

Received: 3 May 2004
Accepted: 23 June 2004

Abstract

Nonlinear approximation of periodic motions around the collinear equilibrium points in the case of the restricted three-body problem when the angular velocity of the primaries is not equal to the value of the classical problem (which is unit in the usual units of mass, length and time), is studied. The stability of the equilibrium points and the analytical solutions in their neighborhood constructing series approximations of the periodic orbits in the planar and in the spatial problem, are given. Families which emanate from L₁, L₂ and L₃ both in the plane and in three dimensions as well as their stability for the Earth-Moon mass distribution, are computed. Special generating plane orbits, the vertical-critical orbits, of the families a, b and c of the problem, are determined and presented. We have also computed series of vertical-critical periodic orbits with the angular velocity as parameter. Three-dimensional families which generate from the bifurcation orbits for , are given.