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Taking both a theoretical and observational perspective, this book is an introduction to recent developments in the field of celestial mechanics. It emphasizes the application to extended celestial bodies and devotes much attention to rotational aspects. In particular, it explains the state of art for accurate modelling of the rotation of celestial bodies such as the Earth, the Moon, and Mercury, which involves principles related to hydrodynamics and geodesy. Comparisons between the light curves of the asteroids and their rotational state are made and spatial techniques leading to the determination of the Earth's gravitational field are explained. Also, the book provides a general overview of the collisional processes in the solar system and of the dynamics of the rings. It is addressed to graduate students and researchers in space sciences and celestial dynamics.
Celestial mechanics. --- Mécanique céleste --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Astronomy - General --- Astrophysics. --- Astronomical physics --- Gravitational astronomy --- Mechanics, Celestial --- Physics. --- Geophysics. --- Mechanics. --- Observations, Astronomical. --- Astronomy --- Space sciences. --- Astronomy, Observations and Techniques. --- Extraterrestrial Physics, Space Sciences. --- Geophysics/Geodesy. --- Observations. --- Cosmic physics --- Physics --- Astrophysics --- Mechanics --- Physical geography. --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Classical Mechanics. --- Geography --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Astronomy—Observations. --- Geological physics --- Terrestrial physics --- Earth sciences --- Science and space --- Space research --- Cosmology --- Science --- Astronomical observations --- Observations, Astronomical
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In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.
Mechanics, Analytic. --- Celestial mechanics. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Analytical mechanics --- Kinetics --- Differentiable dynamical systems. --- Differential Equations. --- Differential equations, partial. --- Dynamical Systems and Ergodic Theory. --- Theoretical, Mathematical and Computational Physics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- Mathematical physics. --- Differential equations. --- Partial differential equations. --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics
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Le but de ce livre est de présenter les développements récents du contrôle géométrique orienté vers la commande (notamment optimale) des véhicules spatiaux. Il est principalement destiné aux étudiants de 3e cycle et aux chercheurs, et son contenu a servi de base à une série de cours de contrôle et d'automatique enseignés à des étudiants de 3e cycle. Il s'appuie sur des projets de recherche avec l'ESTEC et le CNES, sur le contrôle d'attitude d'un satellite, le problème de transfert orbital en temps minimal, et le problème de rentrée atmosphérique d'une navette spatiale. Une première partie est consacrée à une introduction à la mécanique céleste, et la seconde au contrôle des véhicules spatiaux. Un dernier chapitre concerne les méthodes numériques dites indirectes, développées à partir des études des auteurs: méthode de tir et algorithmes de calcul des points conjugués.
Space vehicles --- Celestial mechanics --- Control systems. --- Guidance systems. --- Mathematical models. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Guidance systems (Flight) --- Flight control --- Electronic equipment --- System theory. --- Mathematical optimization. --- Mathematical physics. --- Mechanics. --- Astrophysics. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Methods in Physics. --- Classical Mechanics. --- Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics). --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Physical mathematics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Systems, Theory of --- Systems science --- Science --- Mathematics --- Philosophy --- Systems theory. --- Calculus of variations. --- Physics. --- Space sciences. --- Science and space --- Space research --- Cosmology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Isoperimetrical problems --- Variations, Calculus of
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