Download or read book Symmetries Topology and Resonances in Hamiltonian Mechanics written by Valerij V. Kozlov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Hornstein has written about the author's theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton's laws make music together" (Amer. Math. Monthly, November 1989). Kozlov's book is a systematic introduction to the problem of exact integration of equations of dynamics. The key to the solution is to find nontrivial symmetries of Hamiltonian systems. After Poincaré's work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.
Download or read book Symmetries Topology and Resonances in Hamiltonian Mechanics written by Valerij V. Kozlov and published by . This book was released on 1995-12-12 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Metamorphoses of Hamiltonian Systems with Symmetries written by Konstantinos Efstathiou and published by Springer Science & Business Media. This book was released on 2005 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Mechanics written by John Seimenis and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.
Download or read book Introduction to Mechanics and Symmetry written by Jerrold E. Marsden and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.
Download or read book Chaos Near Resonance written by G. Haller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
Download or read book Symmetry and Perturbation Theory in Nonlinear Dynamics written by Giampaolo Cicogna and published by Springer Science & Business Media. This book was released on 1999-10-19 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented and a perturbative approach is also used. Attention is given to the problem of convergence of the normalizing transformation in the presence of symmetry, with some other extensions of the theory. The results are discussed for the general case of dynamical systems and also for the specific Hamiltonian setting.
Download or read book IUTAM Symposium on Hamiltonian Dynamics Vortex Structures Turbulence written by Alexey V. Borisov and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.
Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,
Download or read book Quasi Periodic Motions in Families of Dynamical Systems written by Hendrik W. Broer and published by Springer. This book was released on 2009-01-25 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.
Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.
Download or read book Quantum Algebras and Poisson Geometry in Mathematical Physics written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 2005 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents applications of Poisson geometry to some fundamental well-known problems in mathematical physics. This volume is suitable for graduate students and researchers interested in mathematical physics. It uses methods such as: unexpected algebras with non-Lie commutation relations, dynamical systems theory, and semiclassical asymptotics.
Download or read book Hamiltonian Chaos and Fractional Dynamics written by George M. Zaslavsky and published by Oxford University Press on Demand. This book was released on 2005 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This books gives a realistic contemporary image of Hamiltonian dynamics, dealing with the basic principles of the Hamiltonian theory of chaos in addition to very recent and unusual applications of nonlinear dynamics and the fractality of dynamics.
Download or read book The Inverse Problem of the Calculus of Variations written by Dmitry V. Zenkov and published by Springer. This book was released on 2015-10-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
Download or read book Mathematical Models and Integration Methods written by Oleg V. Kaptsov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book compiles works presented at a seminar aiming to attract global experts in differential equations, mathematical modeling, and integration methods. It covers classical and contemporary integration techniques for partial differential equations, including Monge and Darboux's approaches and their extensions. Additionally, it introduces a novel theoretical model for plane turbulent flows, presents gravitational equations derived from the principle of least action, and explores symmetry-preserving conservative finite-difference schemes for hydrodynamic-type equations. Analytical solutions for Maxwell's equations in incompressible viscoelastic mediums are examined, alongside theoretical-group analysis of wake mathematical models and reduction to ordinary differential equations. The book also delves into special classes of two-dimensional ideal fluid motion and advancements in discrete orthogonal polynomial theory, showcasing rapid decay properties near interval boundaries. In conclusion, this comprehensive collection is indispensable for researchers and practitioners in applied mathematics, fluid dynamics, and computational modeling, providing valuable insights into cutting-edge methods and solutions in the field.
Download or read book Mathematical Modeling and Supercomputer Technologies written by Dmitry Balandin and published by Springer Nature. This book was released on 2022-12-23 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes selected and revised papers from the 22nd International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2022, held in Nizhny Novgorod, Russia, in November 2022. The 20 full papers and 5 short papers presented in the volume were thoroughly reviewed and selected from the 48 submissions. They are organized in topical secions on computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation.
Download or read book Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations written by Valery V. Kozlov and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.
