On the periodic solutions emerging from the cylindrical precession of an axisymmetric satellite in a circular orbit

In this paper we provide sufficient conditions for the existence of periodic solutions emerging from the cylindrical precession of a symmetrical satellite in a circular orbit having equations of motiond2xdτ2−2dydτ−(4−3α)x=ɛF1τ,x,dxdτ,y,dydτ,d2ydτ2+2dxdτ−y=ɛF2τ,x,dxdτ,y,dydτ,where α and ɛ are real parameters with 1 < α < 4/3. The parameter α = A/C with A and C are the moments of inertia of the symmetrical satellite. On the other hand the parameter ɛ is small and the smooth functions F1 and F2 define the perturbations which are periodic functions in τ and in resonance p:q with some of the periodic solutions of the symmetrical satellite in cylindrical precession, with p and q relatively prime positive integers.