Elimination of the nodes when the satellite is a non spherical rigid body

Abstract

A triaxial rigid body moves in the field of a Newtonian attraction caused by a mass point. The system has six degrees of freedom. We propose a canonical transformation to reduce the degrees of freedom to four. That reduction certainly stems from the symmetries of the problem, in particular from the conservation of the total angular momentum — an invariance often ignored in the problem. The transformation obtained is a change of variables in the phase space, therefore it is independent of the dynamics of the problem and valid for the description of the general motion of a rigid body without restrictions. As an illustration, we carry out an approximate analytical integration of the motion of a quasi-spherical triaxial rigid body in orbit around an attracting center so that the reader is able to see the scope of the reduction in the calculations by using the new variables.