First order normalization in the perturbed restricted three–body problem with variable mass

Abstract

This paper performs the first order normalization that will be employed in the study of the nonlinear stability of triangular points of the perturbed restricted three – body problem with variable mass. The problem is perturbed in the sense that small perturbations are given in the coriolis and centrifugal forces. It is with variable mass as the mass of the third body varies with time. It is found that these perturbations and varying mass are capable to bring a change in the Lagrangian function, and consequently in the basic frequencies. They become successful in affecting the angle coordinates but remain unsuccessful in changing the action momenta coordinates. The transformation utilized for reduction of the second order part of the Hamiltonian to the normal form is also dependent on the perturbed basic frequencies.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 41-46