3rd conference on celestial mechanics. Papers from the conference, Valladolid, Spain, June 8--9, 2000. (Q2768980)

This volume contains the final, written versions corresponding to survey lectures (delivered by the invited speakers M. Lara, J. Palacián and V. Lanchares), oral communications, and contributions in poster form presented at the Conference, which was partly held within the framework of celebrations of the World Mathematical Year 2000.NEWLINENEWLINENEWLINEIn organizing this meeting, priority was given to some current trends, lines of development and open questions in the research activity related to analytical, numerical and qualitative studies in celestial mechanics. Accordingly, the main topics covered by the scientific programme of the Conference attempt to highlight and summarise recent developments and results due to several Spanish groups involved in research activity in celestial mechanics, essentially reflecting advances along three basic lines, namely: bifurcations and chaos in dynamical systems and their applications to celestial mechanics, analytical theories of orbital motion of natural and artificial celestial bodies, and attitude dynamics. NEWLINENEWLINENEWLINEThe papers are arranged and grouped according to the topics and approaches considered in each of them. The first four papers deal with the concept of periodic orbits and its applications to several models, chiefly within the treatment of three- and four-body problems. Next, two communications are concerned with chaotic phenomena, and are followed by a set of four papers devoted to the study of several qualitative and analytical aspects of Hamiltonian dynamical systems. The rotational motion of rigid bodies is considered in the following two articles. Next, the main problem of artificial satellite theory is studied via Delaunay normalisation and Krylov-Bogolyubov-Mitropol'skij method. Canonical treatments of variable-mass two-body systems are presented in the next two papers, the following paper describes the performance of an accelerated-convergence Newton method for numerical solution of nonlinear equations (amongst them, the Kepler equation), and then two communications deal with analytical expansions of geopotential. An invited lecture on the qualitative dynamics of Rydberg-like atomic models (considered as perturbed Keplerian systems), and an investigation of a new type of dynamical instability arising in the study of electrodynamic tethers in inclined orbits constitute the last two papers of this proceedings volume.NEWLINENEWLINENEWLINEContents: \textit{M. Lara} (invited lecture), Un algoritmo para la continuación analítica de órbitas periódicas [An algorithm for analytical continuation of periodic orbits. In Spanish language; abstract in English] (pp. 11-20); \textit{M. A. Andreu}, Towards the computation of pure halo orbits for the real Earth-Moon system (pp. 21-28); \textit{J. Llibre} and \textit{M. Ollé}, Horseshoe periodic orbits for Saturn coorbital satellites (pp. 29-36); \textit{M. Corbera} and \textit{J. Llibre}, Periodic and quasi-periodic orbits for the spatial isosceles three-body problem (pp. 37-44); \textit{J. Aguirre}, \textit{J. C. Vallejo} and \textit{M. A. F. Sanjuán}, Chaotic invariant sets and fractal structures in the Hénon-Heiles system (pp. 45-52); \textit{J. F. Pascual-Sánchez}, Caos en las ecuaciones de Einstein [Chaos in Einstein's equations. In Spanish language; abstract in English] (pp. 53-60); \textit{J. Palacián} and \textit{P. Yanguas} (invited lecture), Asymptotic symmetries and invariant manifolds of perturbed dynamical systems (pp. 61-88); \textit{P. Yanguas} and \textit{J. Palacián}, Normal forms and reduced phase spaces of polynomial Hamiltonians in the plane (pp. 89-96); \textit{M. Iñarrea}, \textit{V. Lanchares}, \textit{A. I. Pascual} and \textit{J. P. Salas}, The dynamics of a three-dimensional Hénon-Heiles-like problem with detuning (pp. 97-102); \textit{A. Riaguas}, \textit{A. Elipe} and \textit{T. López-Moratalla}, Estabilidad orbital en casos resonantes [Orbital stability in resonant cases. In Spanish language; abstract in English] (pp. 103-110); \textit{R. Molina} and \textit{A. Vigueras}, Mejora de la integración analítica de la rotación terrestre usando como modelo un giróstato simétrico [An improvement of the analytical integration of the Earth rotation using a symmetric gyrostatic model. In Spanish language; abstract in English] (pp. 111-118); \textit{A. San Miguel}, Dinámica en el grupo de Lie \(SO_{K}(3)\): Cuerpo rígido forzado [Dynamics in the Lie group \(SO_{K}(3)\): Forced rigid body. In Spanish language; abstract in English] (pp. 119-124); \textit{A. Abad}, \textit{J. F. San Juan} and \textit{S. Serrano}, Método KBM versus normalización de Delaunay [KBM method versus Delaunay normalisation. In Spanish language; abstract in English] (pp. 125-130); \textit{M. Andrade} and \textit{J. Docobo}, Algunos casos de interés del problema de dos cuerpos con masa dependiente del tiempo y de la distancia [Some cases of interest in the two-body problem with mass depending on time and distance. In Spanish language; abstract in English] (pp. 131-136); \textit{L. Floría}, TR-like canonical transformations and perturbed Gylden systems (pp. 137-144); \textit{M. Palacios}, Improving the solution of Kepler's equation and related problems (pp. 145-158); \textit{I. Wytrzyszczak} and \textit{G. Métris}, Direct and fast method of the gravity potential derivatives calculation (pp. 159-170); \textit{I.. Aparicio} and \textit{L. Floría}, On the expansion of the zonal geopotential in DEF focal elements (pp. 171-178); \textit{V. Lanchares} (invited lecture), Bifurcations in Rydberg atoms and analogies with several problems of celestial mechanics (pp. 179-194); \textit{J. Peláez} and \textit{M. Lara}, Influencia de la inclinación orbital en ``tethers'' electrodinámicos [Influence of the orbital inclination in the problem of electrodynamic tethers. In Spanish language; abstract in English] (pp. 195-202).