Download or read book Hamiltonian Perturbation Solutions for Spacecraft Orbit Prediction written by Martín Lara and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Analytical solutions to the orbital motion of celestial objects have been nowadays mostly replaced by numerical solutions, but they are still irreplaceable whenever speed is to be preferred to accuracy, or to simplify a dynamical model. In this book, the most common orbital perturbations problems are discussed according to the Lie transforms method, which is the de facto standard in analytical orbital motion calculations"--Print version, page 4 of cover.
Download or read book Hamiltonian Perturbation Solutions for Spacecraft Orbit Prediction written by Martín Lara and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical solutions to the orbital motion of celestial objects have been nowadays mostly replaced by numerical solutions, but they are still irreplaceable whenever speed is to be preferred to accuracy, or to simplify a dynamical model. In this book, the most common orbital perturbations problems are discussed according to the Lie transforms method, which is the de facto standard in analytical orbital motion calculations.
Download or read book Advances in Nonlinear Dynamics Volume I written by Walter Lacarbonara and published by Springer Nature. This book was released on 2023 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This volume aims to present the latest advancements in experimental, analytical, and numerical methodologies aimed at exploring the nonlinear dynamics of diverse systems across varying length and time scales. It delves into the following topics: Methodologies for nonlinear dynamic analysis (harmonic balance, asymptotic techniques, enhanced time integration) Data-driven dynamics, machine learning techniques Exploration of bifurcations and nonsmooth systems Nonlinear phenomena in mechanical systems and structures Experimental dynamics, system identification, and monitoring techniques Fluid-structure interaction Dynamics of multibody systems Turning processes, rotating systems, and systems with time delays
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1967 with total page 1388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Perturbation Theory for Ultra Differentiable Functions written by Abed Bounemoura and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BRM, and which generalizes the Bruno-R¨ussmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M. Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and MarcoSauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BRM condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity
Download or read book A Geometric Setting for Hamiltonian Perturbation Theory written by Anthony D. Blaom and published by American Mathematical Soc.. This book was released on 2001 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
Download or read book Hamiltonian Systems with Three or More Degrees of Freedom written by Carles Simó and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1968 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perturbation Solutions of the Equations of Motion for a Class of Dual spin Spacecraft written by James Ross Beaty and published by . This book was released on 1986 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Hamiltonian Systems written by Jürgen Moser and published by American Mathematical Soc.. This book was released on 1968 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1985 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1989 with total page 1116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1999 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Perturbation Theory Applied to Planetary Motions written by Ferenc Váradi and published by . This book was released on 1989 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Perturbation Theory of Hamiltonian Systems written by Dmitry Treschev and published by Springer. This book was released on 2010-04-29 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Download or read book Index Aeronauticus written by and published by . This book was released on 1967 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian perturbation theory for optimal trajectory analysis written by William Francis Powers and published by . This book was released on 1966 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
