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Showing 1 to 20 of 56 for “"three-body problem"”.
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Poincaré and the Three Body Problem
… account of Henri Poincare's famous memoir on the three body problem, the final version of which was published in <i>Acta Mathematica</i> in 1890 as the prize-winning entry in King Oscar II's 60th birthday competition. The memoir is reknowned both for its role in providing the foundations for …
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Transport geometry of the restricted three-body problem
This dissertation expands across three topics the geometric theory of phase space transit in the circular restricted three-body problem (CR3BP) and its generalizations. The first topic generalizes the low energy transport theory that relies on linearizing the Lagrange points in the CR3BP to …
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Constrained Motion Analysis of Spacecraft Trajectory in Restricted Three Body Problem
… dynamics as applied to the restricted three-body problem of the Sun-Earth-Spacecraft. A dynamic model of the restricted three-body system is presented to analyze the unconstrained motion of spacecraft. The results show the instability due to perturbation from the SRP. Then, the …
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A Low-Complexity Algorithm for Trajectory Generation in the Three-Body Problem
… methods of trajectory generation in this multi-body dynamical system for computationally limited systems. Thus, a low-complexity classical algorithm is proposed to achieve accurate orbital trajectories in the three-body problem. The proposed algorithm solves a polynomial interpolation problem, …
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Coupled orbit-attitude mission design in the circular restricted three-body problem
<p>Trajectory design increasingly leverages multi-body dynamical structures that are based on an understanding of various types of orbits in the Circular Restricted Three-Body Problem (CR3BP). Given the more complex dynamical environment, mission applications may also benefit from deeper insight …
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Trajectory design in the spatial circular restricted three-body problem exploiting higher-dimensional Poincare maps
… vicinity of the primary bodies in the spatial problem. Because current strategies to represent higher-dimensional maps, generally, lead to a loss of information, new approaches to represent all information contained in higher-dimensional Poincaré maps are sought. ^ The field of data …
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Spacecraft Orbit Design in the Circular Restricted Three-Body Problem Using Higher-Dimensional Poincaré Maps
<p>Strategies for designing three-dimensional spacecraft trajectories in a multi-body dynamical environment are investigated using four-dimensional Poincaré maps. Unlike the planar circular restricted three-body problem, where a two-dimensional map provides a simplified view of a portion of the …
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Human As We All Are: Posthuman Subjectivity in The Paper Menagerie and The Three-Body Problem
… virtual reality and BCI in Cixin Liu’s <em>The Three-Body Problem</em> both extend, and reveal the ultimate shortcomings of, human subjectivity.</p>
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Using the Circular Restricted Three-Body Problem to Design an Earth-Moon Orbit Architecture for Asteroid Mining
… resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit …
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ΠΕΡΙΟΔΙΚΕΣ ΚΑΙ ΑΣΥΜΠΤΩΤΙΚΕΣ ΛΥΣΕΙΣ ΓΥΡΩ ΑΠΟ ΑΣΤΑΘΗ ΣΗΜΕΙΑ ΙΣΟΡΡΟΠΙΑΣ ΣΤΟ ΠΡΟΒΛΗΜΑ ΤΩΝ ΤΡΙΩΝ ΣΩΜΑΤΩΝ
… SYSTEMS ARE AMONG OTHERS, THE CLASSICAL "THREE BODY PROBLEM" AND ITS SIMPLIFIED VERSIONS KNOWN AS THE (CIRCULAR) "RESTRICTED THREE-BODY PROBLEM" AND THE "ELLIPTIC RESTRICTED THREE- BODY PROBLEM". THISTHESIS CONSISTS OF EIGHT CHAPTERS: IN CHAPTER 1 WE GIVE THE EQUATIONS OF MOTION OF THE …
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ΑΝΑΛΥΤΙΚΗ ΚΑΙ ΑΡΙΘΜΗΤΙΚΗ ΜΕΛΕΤΗ ΤΩΝ ΠΕΡΙΟΔΙΚΩΝ ΛΥΣΕΩΝ ΤΟΥ ΠΡΟΒΛΗΜΑΤΟΣ ΤΩΝ ΤΡΙΩΝ ΣΩΜΑΤΩΝ
… DISSERTATION IS THE PERIODIC SOLUTIONS OF THE THREE-BODY PROBLEM IN TWO AND THREE DIMENSIONS AND, IN PARTICULAR, THE DETERMINATION OF THESE SOLUTIONS BY ANALYTIC APPROXIMATIONS AND NUMERICAL METHODS. IN THE FIRST PART (CHAPTERS 1 TO 5) WE STUDY ANALYTICALLY AND NUMERICALLY THE PERIODIC …
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Semiclassical Scattering for Two and Three Body Systems
… present a brief mathematical discussion of the three body problem, first in classical mechanics and then in quantum mechanics. Finally using an approach similar to the semiclassical wave-packet construction we form a semiclassical approximation to the solution of the Schrödinger equation for the …
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Coupled Dynamics in the Cislunar Region and Spacecraft Attitude Prediction in a Higher-Fidelity Model
… cislunar region of space is a complex, multi-body dynamical environment that cannot be modeled trivially. Traditional point-mass assumptions made to simplify the mission design process may be insufficient for accurately predicting spacecraft motion in environments where orbit-attitude coupling …
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Periodic solutions of nonlinear wave equations
… H. Poincare in the memoire he presented on the three body problem. By looking at periodic and asymptotics solutions he discovered what today we call chaos, and showed that these special solutions were a powerful tool to resolve questions in the theory of ordinary differential equations.
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Robust Adaptive Rigid Body State and Mass Property Estimation Via Unscented Kalman Filter on TSE(3) with Process Noise Estimation
… moment of inertia, is a crucial yet challenging problem in spacecraft autonomy and astrodynamics. Knowledge of mass properties of a spacecraft is essential for future astronautical missions, as changes in the mass properties of a spacecraft due to a shift in cargo distribution often require a …
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Exploring recurrences in quasiperiodic systems
… was introduced to study the restricted three body problem and it is very useful for the characterization of nonlinear systems. I have analyzed in detail the recurrence patterns of systems with quasiperiodic dynamics both analytically and numerically. Based on a theoretical analysis, I …
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Mathematical methods in atomic physics = Métodos matemáticos en física atómica
Los problemas de dispersión de partículas, como son los de dos y tres cuerpos, tienen una relevancia crucial en física atómica, pues permiten describir diversos procesos de colisiones. Hoy en día, los casos de dos cuerpos pueden ser resueltos con el grado de precisión numérica que se desee. Los …
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Low thrust augmented periodic orbits in the two- and three-body problems
… libration points in the circular restricted three-body problem. In the Earth-Moon system, position-only feedback is used to stabilise the local dynamics, and interesting new multiply-periodic orbits are generated. The in-plane and out-of plane natural frequencies are then synchronised, …
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A new numerical optimization method based on Taylor series for challenging trajectory optimization problems
New methods to solve trajectory optimization problems are devised. The methods use direct transcription to convert the continuous optimal control problem into a parameter optimization problem that can be solved with non-linear programming. In direct transcription the system equations must be …
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