1,721,141 research outputs found
Close approaches and the border of stable secular motions in the Restricted 3-Body Problem
No full textLo scopo principale della presente tesi consiste nel proporre, nell'ambito del problema dei tre corpi ristretto, una nuova definizione del limite che discrimina tra il regime di moto governato dalla teoria secolare classica e gli altri tipi di regime, in cui questi ultimi risultano essenzialmente influenzati o dalla presenza di incontri ravvicinati o da interazioni risonanti della particella di massa trascurabile (p.e. un asteroide) con il perturbatore primario (p.e. Giove). Tale obiettivo viene raggiunto operando sui seguenti fronti:
i) Esploriamo all'inizio la possibilità di tenere conto di opportuni metodi di regolarizzazione in prossimità delle singolarità gravitazionali: si introduce così un'estensione hamiltoniana della regolarizzazione di Kustaanheimo-Stiefel al problema ellittico ristretto degli N corpi mediante una riduzione simplettica dello spazio delle fasi esteso. Dopo una breve rassegna dello stato dell'arte sulle tecniche di regolarizzazione, la teoria viene sviluppata per N=3 e testata numericamente. In particolare forniamo un'implementazione della teoria nella propagazione di orbite aventi incontri ravvicinati con il perturbatore primario. Tale implementazione si dimostra migliorativa in termini di accuratezza delle prestazioni numeriche durante l'integrazione laddove necessario, indipendentemente dalla complessità del modello a tre corpi considerato (piano/spaziale, circolare/ellittico).
ii) Passiamo ora al contesto della teoria perturbativa canonica hamiltoniana e presentiamo un approccio in forma chiusa (cioè senza espandere nelle potenze delle eccentricità) senza l'uso dell'algoritmo di ''relegation'' per particelle con traiettorie non intersecanti esterne alla traiettoria del perturbatore primario, comprese quelle altamente eccentriche.
iii) A questo punto ci si prefigge di identificare e caratterizzare topologicamente le regioni di stabilità a lungo termine (secolari) in sezioni appropriate dello spazio delle fasi tramite diverse mappe di stabilità numerica. Discutiamo l'applicabilità del metodo come criterio per stimare la frontiera dei suddetti domini per orbite lontane da quella di Giove quando il pianeta è assunto in orbita circolare e confrontiamo il risultato con altri criteri euristici esistenti.
iv) In qualità di risultato complementare, le suddette mappe di stabilità rivelano un'architettura orbitale assai più ricca costituita da una "struttura ornamentale" di varietà generate dal pianeta e collegate in una serie di archi che si estendono per l'intero Sistema Solare. Indaghiamo così le implicazioni di queste strutture riguardo alla dinamica dei corpi minori. Come caso di riferimento consideriamo il noto problema aperto nel nostro sistema solare relativo all'asimmetria osservata nel numero e nella distribuzione nello spazio delle fasi degli asteroidi troiani attorno ai punti di equilibrio equilateri di Giove L4 ed L5. Si discutono i possibili collegamenti di questo fenomeno con un'asimmetria rilevata che interessa le intersezioni eterocline tra le varietà stabili e instabili delle orbite periodiche di Lyapunov attorno ai punti lagrangiani L1, L2 ed L3. Mostriamo come tali intersezioni influenzino il flusso di particelle nella regione troiana e proponiamo un meccanismo plausibile di intrappolamento dei corpi in presenza di un processo di migrazione planetaria approssimativamente adiabatico.The central goal of the present thesis consists in proposing a novel threshold, in the context of the restricted three-body problem, capable to discriminate between the regime of motion governed by the classic secular theory and the rest of regimes, which are mainly influenced either by close encounters or by resonant interactions of the test particle (e.g. asteroid) with the primary perturber (e.g. Jupiter). This goal is reached operating on the following fronts:
i) We explore at the beginning the possibility to take into account suitable regularization methods in the vicinity of the gravitational singularities: we introduce a Hamiltonian extension of the Kustaanheimo-Stiefel regularization to the elliptic restricted N-body problem by means of a symplectic reduction of the extended phase space. After a short review of the state of the art on regularization techniques, we develop the theory for N=3 and test it numerically. In particular, we provide an implementation of the theory in the propagation of the orbits having close encounters with the primary perturber. This is shown to usefully improve the performance of numerical integrations when needed, regardless the complexity of the three-body model considered (planar/spatial, circular/elliptic).
ii) We pass to the machinery of Hamiltonian canonical perturbation theory and present a closed-form approach (i.e. without expanding in powers of the eccentricities) without use of relegation for particles with non-crossing trajectories exterior to the primary perturber's trajectory, including those highly eccentric.
iii) At this point, we address the question of identifying and topologically characterizing the long-term (secular) stability regions in appropriate sections of the phase space via different numerical stability maps. We discuss, then, the applicability of the above closed-form method as a criterion for estimating the boundary of such domains for orbits further than Jupiter's when the planet is assumed on a circular orbit and compare the result to other existent heuristic criteria.
iv) As a side result from the above analysis, the aforementioned stability maps reveal a much richer orbital architecture consisting in an ''ornamental structure'' of manifolds generated by the planet connected in a series of arches that spread throughout the whole Solar System. We then investigate the implications of these structures for small body dynamics. As a pivotal case, we consider the well-known open problem of the observed asymmetry in the number and phase-space distribution of Trojan asteroids around Jupiter’s equilateral equilibrium points L4 and L5 in our solar system. We discuss possible links of this problem to a detected asymmetry in the heteroclinic intersections between the unstable and stable manifolds of the Lyapunov orbits around the Lagrangian points L1, L2 and L3. We show how these intersections influence the inflow of particles to the Trojan region, and propose a plausible trapping mechanism of the bodies under an approximately adiabatic process of planetary migration
A Kustaanheimo–Stiefel regularization of the elliptic restricted three-body problem and the detection of close encounters with fast Lyapunov indicators
Full text linkWe present the Kustaanheimo–Stiefel (KS) regularization of the elliptic restricted three-body problem (ER3BP) at the secondary body , and discuss its use to study a category of transits through its Hill’s sphere (fast close encounters). Starting from the Hamiltonian representation of the problem using the synodic rotating–pulsating reference frame and the true anomaly of as independent variable, we perform the regularization at the secondary body analogous to the circular case by applying the classical KS transformation and the iso-energetic reduction in an extended 10-dimensional phase-space; this translates into an efficient algorithm that can be readily implemented to numerically integrate the equations of motion. Using such a regularized Hamiltonian we recover a definition of fast close encounters in the ER3BP for small values of the mass parameter (while we do not require a smallness condition on the eccentricity of the primaries), and we show that for these encounters the solutions of the variational equations are characterized by an exponential growth during the fast transits through the Hill’s sphere. Thus, for small , we justify the effectiveness of the regularized fast Lyapunov indicators (RFLIs) to detect orbits with multiple fast close encounters. Finally, we provide numerical demonstrations and show the benefits of the regularization in terms of the computational cost
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
Discrete multi-layer estimator implementation for sensorless control of elastic drive systems - An industrial case study
No full textSensorless AC drives do not require speed sensor and have the advantage of high reliability and low cost. The sensorless control techniques require the estimation of internal state variables and the accuracy of this estimation influences the overall control performances. Moreover, implementation of a state observer which computes speed signal and the use of digital filter introduce intrinsic delays which affect electrical drive performances. The result is a deterioration of control performances even if control parameters are correctly tuned. The control of a dual-inertia elastic system is a critical application because of the undesired mechanical oscillations and its sensitivity to motor speed feedback estimation. This paper presents a multi-layer estimator to control a dual inertia elastic system
Latency effect in a variable speed control on torsional response of elastic drive systems
No full textTorsional vibration issues in elastic drive systems are a well-known topic also in the industrial field. The torque pulsations produced by the drive are the main causes of these torsional resonance excitations. However, it will be analysed in this paper how some side-effects in the control strategy, like the latencies, are critical as the torque ripple. Indeed, the suppression of this vibrations phenomenon cannot be achieved correctly without analysing and quantifying the time-delays that affect the system. This paper aims to provide both a comprehensive analysis on such latencies and introduces a method to proof the relationship between the damping capability of the process and the time-delays. It will be defined a process damping coefficient in order to explain the relations between the electrical damping, related to the control architecture, the latencies and the mechanical damping
Experimental Comparison of Speed-Dependent Rolling Coefficients in Small Cycling Tires
No full textIn this article, the methodology and results of an experimental campaign on small and slick bicycle tires are presented. The test was developed to compare the rolling resistance of tires to be used in high-speed competitions for streamlined human-powered vehicles. After an explanation of the theoretical background for the measurement, the test-rig and the adopted procedure to measure and subtract aerodynamic effects are presented. The obtained data show that the rolling resistance coefficient has a nonlinear dependency from the speed between 45 and 145 km/h. The data comparison points out a decrease in rolling losses up to 54% by switching from a butyl to latex inner tube on the same tire, whereas no significant difference is detected between the latex tube and tubeless configuration. An estimation of the impact on racing performance is provided, showing that selecting the best option could save up to 19% of the overall effort energetic cost, which means a higher final speed can be achieved with the same rider effort. Finally, a speculative analysis is proposed that considers different functions to fit the obtained data, pointing out the need for experimental measurements on the very-low-speed region to achieve a better understanding of the entire rolling resistance behavior with respect to speed
Explicit Computation of Indirect Hybrid MPC for Voltage Control in Multilevel DC-DC Converters
No full textThis paper extends indirect model predictive control (MPC) to the design of a three-level neutral point clamped (3L-NPC) step-down dc-dc converters. A hybrid model is used to map the switching pattern of two switches only and to build piecewise affine (PWA) decoupled models with reduced complexity. Two constrained optimization problems are explicitly solved offline to provide two explicit MPCs driven by a wake-up logic. The resulting approach represents a first step towards the extension of explicit MPC to more complex multilevel topologies, when a reduced computational effort is required
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