An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct ...

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By ...

Low-altitude, near-polar orbits are very desirable for scientific missions to study the natural satellites of the planets of the Solar System, such as Europa, that is one of the natural satellites of Jupiter. The problem ...

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a ...

The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for ...

This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up ...

In the present work we consider a dynamical system of mum size particles around the Earth subject to the effects of radiation pressure. Our main goal is to study the evolution of its relative velocity with respect to the ...

In this paper singularly perturbed reversible vector fields defined in R-n without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and ...