Tag: Hamiltonian

Free Download Symmetries, Topology and Resonances in Hamiltonian Mechanics By Valerij V. Kozlov (auth.)
1996 | 378 Pages | ISBN: 3642783953 | PDF | 11 MB
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.

Free Download Hamiltonian Dynamical Systems: History, Theory, and Applications By Craig G. Fraser (auth.), H. S. Dumas, K. S. Meyer, D. S. Schmidt (eds.)
1995 | 385 Pages | ISBN: 1461384508 | PDF | 15 MB
From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

Free Download Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations By Calvin D. Ahlbrandt, Allan C. Peterson (auth.)
1996 | 376 Pages | ISBN: 1441947639 | PDF | 8 MB
This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.

Free Download Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935-2008) by Albert C. J. Luo, Valentin Afraimovich
English | PDF | 2010 | 312 Pages | ISBN : 3642127177 | 33.8 MB
"Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935-2008)" covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.

Free Download Metamorphoses of Hamiltonian Systems with Symmetries by Konstantinos Efstathiou
English | PDF | 2005 | 155 Pages | ISBN : 354024316X | 3.5 MB
Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Free Download Classical Mechanics: Systems of Particles and Hamiltonian Dynamics by Walter Greiner
English | PDF (True) | 2010 | 574 Pages | ISBN : 3642034330 | 7.5 MB
This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems.