Francisco Javier Molero

University of Murcia | UM · Department of Applied Matematics

We address the attitude dynamics of a triaxial rigid body in a circular orbit. This task is done by means of an intermediary model, which is obtained by splitting the Hamiltonian in the form H=H0+H1 where H0 is required to be a non-degenerate integrable Hamiltonian system. A numerical study is presented comparing the dynamics of the new intermediar...

We study the roto-orbital dynamics of a uniform sphere and a body with axial symmetry by means of a radial intermediary, which defines an integrable system. Numerical comparisons of the MacCullagh’s truncation of the gravity gradient potential and intermediary models are performed, concluding that the intermediary provides a valuable approximation...

We live in a highly volatile technological environment, in which the generation of new data and information access tools has increased the level of specialization of the users’ information needs. In this changeable scenario, standards and the role of librarians must also evolve along with the services provided to users. The lack of specialization i...

Poisson and integrable systems are orbitally equivalent through the Nambu bracket. Namely, we show that every completely integrable system of differential equations may be expressed into the Poisson-Hamiltonian formalism by means of the Nambu-Hamilton equations of motion and a reparametrisation related by the Jacobian multiplier. The equations of m...

Analytic and numeric comparisons of the solution of Euler equations for the free rigid body problem are accomplished, after applying two linearizations. The one proposed by Molero et al. makes use of a solution in trigonometric functions whereas the other one comes as an application of a recent theorem by Llibre et al. and expresses it in exponenti...

We study the integrable system of first order differential equations $\omega_i(v)'=\alpha_i\,\prod_{j\neq i}\omega_j(v)$, $(1\!\leq i, j\leq\! N)$ as an initial value problem, with real coefficients $\alpha_i$ and initial conditions $\omega_i(0)$. The analysis is based on its quadratic first integrals. For each dimension $N$, the system defines a f...

Enhancing content description of specialized resources, particularly astronomical resources, is a matter that is still unresolved in library and information science. In this paper, the authors outline deficiencies in some fields and elements of cataloging standards for description of historical astronomical resources, mainly star atlases and catalo...

Archivos y bibliotecas astronómicas de todo el mundo albergan miles de documentos históricos en soportes no electrónicos, los cuales contienen valiosa información a la que es muy difícil acceder de forma selectiva, debido a la insuficiente descripción documental que suele realizarse del contenido de estos recursos en las bases de datos de estas ins...

Relative equilibria of an intermediary in attitude dynamics of a generic triaxial spacecraft in a circular orbit under gravity-gradient perturbation are discussed. Intermediary defines a Poisson flow over a large parameter space: three physical parameters (moments of intertia) and three distinguished parameters, the integrals M,G3 and n. In the cas...

In this paper two Hamiltonian intermediaries H{ν,φ} and Hν for the gravity-gradient attitude dynamics of a generic triaxial satellite are formulated using Andoyer variables. Assuming the satellite in a circular orbit, both models allow to analyze the coupling between the orbital mean motion and rotational variables and the role played by the moment...

Using Andoyer's variables we present a new proof of Montgomery's formula by measuring Δμ when ν has made a rotation. Our treatment is built on the equations of the differential system of the free rigid solid, together with the explicit expression of the spherical area defined by the intersection of the surfaces given by the energy and momentum inte...

Some intermediary models for the study of roto-translatory dynamics of a triaxial rigid body under gravity-gradient torque are considered assuming MacCullagh’s approximation. Following Poincar´e and Arnold, they are obtained by splitting the Hamiltonian in the form H = H0 + H1 where each intermediary H0 defines a non-degenerate integrable 1-DOF Ham...

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundament...

K. Meyer has advocated for the study of elliptic functions and integrals from a dynamical systems point of view. Here, we follow his advice and we propose the bidimensional Hamiltonian Duffing oscillator as a model; it allows us to deal with the elliptic integral of third kind directly. Focusing on bounded trajectories we do a detailed analysis of...