Translatory-Rotatory Motion of a Gyrostat in a Newtonian Force Field

Abstract

In this communication, the problem of the translatory-rotatory motion of two gyrostats G₁, G₂, whose elementary particles act upon each other according to Newton’s law is formulated. Following several changes of variables, the Hamiltonian function is expressed in a set of modified canonical variables of Delaunay and Audoyer, in order to find out the influence of the internal stationary motions — which do not modify the distribution of mass of the bodies — over their rototranslatory motion.

Then, we consider one of the gyrostats as a spherical rigid body and the other as a symmetric gyrostat whose distribution of mass is quasi-spherical. Assuming that one of the components of the gyrostatic momentum is greater than the others, and after straightforward eliminations and changes of variables, the problem is integrated up to the first order of perturbation by means of Deprit’s method, the periodical and secular perturbations being obtained independently for both orbital and rotational motions.