1,721,228 research outputs found
Integrability of close encounters in the spatial restricted three-body problem
Full text linkWe extend to the spatial case a technique of integration of the close encounters formulated by Tullio Levi-Civita for the planar restricted three-body problem. We consider the Hamiltonian introduced in the Kustaanheimo-Stiefel regularization and construct a complete integral of the related Hamilton-Jacobi equation by means of a series convergent in a neighborhood of the collisions with the primary or secondary body
On the limits of application of mean motion resonant normal forms of the three-body problem for crossing orbits and close encounters
No full textIn this paper, we study the limits of application of canonical perturbation theory, specifically the validity of the normal form approximations, for the study of the mean motion resonances of the planar circular restricted three-body problem in the domain of orbits which cross, or are close to cross, the orbit of the secondary body. First, we discuss analytic issues related to the definition of a MMR normal form within a domain of the phase-space to which these orbits belong; then, we compute with a numerical method the canonical transformations defining the MMR normal forms. The limits of validity of the averaging method are studied by supplementing the information provided by the phase-portrait representations of the normal form Hamiltonian with analyses concerning the preservation of the quasi-integrals of motion obtained through one step of perturbation theory, and the computation of fast Lyapunov indicators regularized with respect to the close encounters with the secondary body. ..
Transits close to the Lagrangian solutions L1, L2 in the elliptic restricted three-body problem
Full text linkIn the last decades a peculiar family of solutions of the circular restricted three body problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit close to the Lagrangian points L 1, L 2 of the CRTBP, have been classified using the values of approximate local integrals and of the Jacobi constant. The use for small bodies of the Solar System requires to consider a hierarchical extension of the model, from the CRTBP to the full N planetary problem. The elliptic restricted three body, which is the first natural extension of the CRTBP, represents already a challenge, since global first integrals such as the Jacobi constant are not known for this problem. In this paper we extend the classification of the transits occurring close to the Lagrangian points L 1, L 2 of the ERTBP using a combination of the Floquet theory and Birkhoff normalizations. Provided that certain non-resonance conditions are satisfied, we conjugate the Hamiltonian of the problem to an integrable normal form Hamiltonian with remainder, which is used to define approximate local first integrals and to classify the transits of orbits through a neighbourhood of the Lagrange equilibria according to the values of these integrals. We provide numerical demonstrations for the Earth-Moon ERTBP
Cantori of the dissipative sawtooth map
No full textWe investigate the existence of cantori for a dissipative version of the sawtooth map. Making use of an explicit parametric representation of the solution, we prove that cantori exist for any irrational value of the frequency. We also perform a numerical study aimed to determine some dynamical properties of the dissipative sawtooth map
The steep Nekhoroshev's Theorem and optimal stability exponents (an announcement)
No full textA new statement of Nekhoroshev’s theorem in the general steep case with
stability exponents, conjectured to be optimal, is presented
Interplanetary transfers using stable and unstable manifold tubes originating at L1 and L2 in the elliptic restricted three-body problems
No full textThe solutions originating at the Lagrangian points L1 and L2 of the restricted three-body problem are used in space flight dynamics to find useful station-keeping orbits as well as convenient low-energy transfers between planets and satellites of the Solar System. The circular restricted three-body problem (CR3BP) provides the simplest model where the Lagrangian points, as well as the related stable and unstable manifold tubes, are defined. Nevertheless, their use for Solar System applications requires to consider hierarchical extensions of the model. The elliptic restricted three-body problem (ER3BP) is the most important extension to consider for space flight dynamics. In this paper we discuss the differences of the manifold tubes of the ER3BP with respect to the CR3BP which have an impact in the transfers between orbits in the manifold tubes related to different planets. We find that there is a threshold value for the eccentricity of the planet, depending on its reduced mass, which changes drastically the distribution of the longitudes of the first pericenter (or apocenter) of the orbits in the manifold tubes leaving or approaching the Lagrangian points L1, L2. For example, such a difference changes the design of the Hohmann transfers between two orbits of the manifold tubes when the planets Mercury or Mars are concerned
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
