Andrés Riaguas

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• Professor (Associate) at University of Valladolid

This work studies the motion around irregular elongated asteroids through two approaches. Firstly, it revisits the dipole-segment model, identifying families of periodic orbits for asymmetric mass distribution. Additionally, a new model incorporating variable density for elongated asteroids is introduced and compared to the dipole-segment model. Se...

This paper discusses the dynamics of particles orbiting planetary rings under a general central potential. Starting with the mathematical description of the dynamical system, we analyze the motion of a particle with infinitesimal mass as attracted by a central body surrounded by a homogeneous circular annular disk. Throughout the paper we carry out...

This paper studies the main features of the dynamics around a planar annular disk. It is addressed an appropriated closed expression of the gravitational potential of a massive disk, which overcomes the difficulties found in previous works in this matter concerning its numerical treatment. This allows us to define the differential equations of moti...

This paper studies the main features of the dynamics around a planetary ring composed by a massive planar annulus and a central body. Based on previous analysis where we analyzed the motion of satellite with infinitesimal mass as attracted by an isolated planar annulus, we raise the question of the dynamics around a central body surrounded by a hom...

This paper studies the main features of the dynamics around a massive annular disk. The first part addresses the difficulties finding an appropriated expression of the gravitational potential of a massive disk, which will be used to define the differential equations of motion of our dynamical system. The second part describes the main features of t...

This article studies the main features of the dynamics around an annular disk. The first part addresses the difficulties finding a usable expression of the gravitational potential of a massive disk that will be used later on to define the differential equations of motion of our dynamical system. The second part of the article describes the dynamics...

This article studies the main features of the dynamics around a massive annular disk. The first part addresses the difficulties finding an appropriated expression of the gravitational potential of a massive disk, which will be used later on to define the differential equations of motion of our dynamical system, and for the algorithms computing fami...

We study the properties of the figure-8 periodic solution in the planar three-body problem with equal masses. The three masses have a triple overlap orbit: they travel over one and the same geometric curve.This solution also has the classical isosceles symmetry property. Therefore, we study the relative periodic solutions in a rotating frame, the w...

A canonical transformation is proposed to handle Hamiltonian systems made of the addition or subtraction of three harmonic oscillators in p:q:r resonance. This transformation is an extension of the classical Lissajous transformation for the 1:1 resonance. Our extended Lissajous variables consist of three pairs of action-angle variables, which makes...

We consider the anisotropic Hamiltonian systems which potential is made of a finite sum of homogeneous parts of arbitrary degree. For this problem, we prove for two and three degrees of freedom, that there are no more meromorphic integrals than the Hamiltonian itself, except for the classical integrable cases.

In this paper we analyze the orbital stability of the equilibria cor- responding to the motion of point mass under the gravitational field of a massive finite segment. This potential is expressed in closed form as a logarithmic function, depending on the distance of the particle to the end-points of the segment. This model may be considered as an a...

We study nonlinear stability of equilibria corresponding to the motion of a particle orbiting around a finite straight segment. The potential is a logarithmic function, and may be considered as an approximation to the potential generated by elongated celestial bodies. By means of Arnold’s theorem for non-definite quadratic forms, we determine the o...

In systems with two degrees of freedom, Arnold's theorem is used for studying nonlinear stability of the origin when the quadratic part of the Hamiltonian is a nondefinite form. In that case, a previous normalization of the higher orders is needed, which reduces the Hamiltonian to homogeneous polynomials in the actions. However, in the case of reso...

Analysis of lineaments from satellite images normally includes the determination of their orientation and density. The spatial variation in the orientation and/or number of lineaments must be obtained by means of a network of cells, the lineaments included in each cell being analysed separately. The program presented in this work, LINDENS, allows t...

In this paper, we consider the motion of a particle under the gravitational field of a massive straight segment. This model is used as an approximation to the gravitational field of irregular shaped bodies, such as asteroids, comet nuclei and planets's moons. For this potential, we find several families of periodic orbits and bifurcations.

We analyse the phase flow evolution of the torque free asymmetric gyrostat motion. The gyrostat consists of a triaxial rigid body and a symmetric rotor spinning around one of the principal axis of inertia of the gyrostat. The problem is converted into a two parametric quadratic Hamiltonian with the phase space on the sphere. As the parameters evolv...

In this paper, we consider the motion of a particle under the gravitational field of a massive straight segment. This model is used as an approximation to the gravitational field of irregular shaped bodies, such as asteroids, comet nuclei and planets’s moons. For tbis potential, we find several families of periodic orbits and bifurcations.

Tres palabras clave: perfil de ingreso, evaluación, matemáticas. Resumen. Un aspecto esencial en la formación, del tipo que sea, es conocer la población a la que está dirigida; en nuestro caso, los estudiantes de nuevo acceso a los estudios de Ingeniería. Hemos recogido información de lo que se consigue en la educación matemática preuniversitaria e...