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Author | : Frank H. Clarke |
Publisher | : |
Total Pages | : 26 |
Release | : 1979 |
Genre | : Boundary value problems |
ISBN | : |
Download Nonlinear Oscillations and Boundary-Value Problems for Hamiltonian Systems Book in PDF, ePub and Kindle
Hamilton's differential equations are basic in the study of theoretical mechanics. A particular class of motions of interest for such systems of equations are the periodic ones, which correspond to oscillations (vibrations) of the underlying physical system; the absence of such motions is usually associated with resonance phenomena. In this paper we give conditions on the Hamiltonian function H which guarantee the existence of periodic orbits, as well as other more general types of motions. One distinction with previous work on the subject is that we consider forced vibrations arising from external driving forces; another is that the solutions in question are characterized directly as the solutions of a specific minimization problem (i.e., we obtain a 'variational principle'), a feature which could prove useful for computational purposes.
Author | : Russell Johnson |
Publisher | : Springer |
Total Pages | : 515 |
Release | : 2016-03-25 |
Genre | : Mathematics |
ISBN | : 3319290258 |
Download Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control Book in PDF, ePub and Kindle
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
Author | : Ernesto A Lacomba |
Publisher | : World Scientific |
Total Pages | : 218 |
Release | : 1993-04-30 |
Genre | : |
ISBN | : 9814553166 |
Download Hamiltonian Systems And Celestial Mechanics Book in PDF, ePub and Kindle
This volume puts together several important lectures on the Hamiltonian Systems and Celestial Mechanics to form a comprehensive and authoritative collection of works on the subject. The papers presented in this volume are an outgrowth of the lectures that took place during the 'International Symposium on Hamiltonian Systems and Celestial Mechanics', which was held at the CIMAT (Centro de Investigacion en Matematicas, Guanajuato, Mexico) from September 30 to October 4, 1991. In general, the lectures explored the subject of the Hamiltonian Dynamics and Celestial Mechanics and emphasized its relationship with several aspects of topology, mechanics and dynamical systems.
Author | : Ioėlʹ Gilʹevich Malkin |
Publisher | : |
Total Pages | : 480 |
Release | : 1959 |
Genre | : Oscillations |
ISBN | : |
Download Some Problems in the Theory of Nonlinear Oscillations Book in PDF, ePub and Kindle
Author | : Sergej B. Kuksin |
Publisher | : Springer |
Total Pages | : 128 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540479201 |
Download Nearly Integrable Infinite-Dimensional Hamiltonian Systems Book in PDF, ePub and Kindle
The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.
Author | : Stavros C. Farantos |
Publisher | : Springer |
Total Pages | : 165 |
Release | : 2014-09-22 |
Genre | : Science |
ISBN | : 3319099884 |
Download Nonlinear Hamiltonian Mechanics Applied to Molecular Dynamics Book in PDF, ePub and Kindle
This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.
Author | : Solomon Lefschetz |
Publisher | : Princeton University Press |
Total Pages | : 128 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400882702 |
Download Contributions to the Theory of Nonlinear Oscillations (AM-29), Volume II Book in PDF, ePub and Kindle
These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Author | : Lamberto Cesari |
Publisher | : Princeton University Press |
Total Pages | : 299 |
Release | : 1960-01-21 |
Genre | : Mathematics |
ISBN | : 0691079331 |
Download Contributions to the Theory of Nonlinear Oscillations Book in PDF, ePub and Kindle
Classic contributions to the theory of nonlinear oscillations from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author | : Carles Simó |
Publisher | : Springer Science & Business Media |
Total Pages | : 690 |
Release | : 1999-06-30 |
Genre | : Mathematics |
ISBN | : 9780792357100 |
Download Hamiltonian Systems with Three or More Degrees of Freedom Book in PDF, ePub and Kindle
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.
Author | : Ivar Ekeland |
Publisher | : |
Total Pages | : 21 |
Release | : 1979 |
Genre | : Hamiltonian systems |
ISBN | : |
Download Forced Oscillations of Nonlinear Hamiltonian Systems Book in PDF, ePub and Kindle