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Author: Valeriĭ Viktorovich Kozlov Publisher: American Mathematical Soc. ISBN: 9780821804278 Category : Mathematics Languages : en Pages : 268
Book Description
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics.
Author: Valeriĭ Viktorovich Kozlov Publisher: American Mathematical Soc. ISBN: 9780821804278 Category : Mathematics Languages : en Pages : 268
Book Description
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics.
Author: Jerry B. Marion Publisher: Academic Press ISBN: 1483272818 Category : Science Languages : en Pages : 593
Book Description
Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.
Author: V.I. Arnol'd Publisher: Springer Science & Business Media ISBN: 1475720637 Category : Mathematics Languages : en Pages : 530
Book Description
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Author: J.M. Souriau Publisher: Springer Science & Business Media ISBN: 1461202817 Category : Mathematics Languages : en Pages : 427
Book Description
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
Author: Jorge V. José Publisher: Cambridge University Press ISBN: 9780521636360 Category : Science Languages : en Pages : 702
Book Description
A comprehensive graduate-level textbook on classical dynamics with many worked examples and over 200 homework exercises, first published in 1998.
Author: Victor V. Kozlov Publisher: Springer Science & Business Media ISBN: 9783540422075 Category : Science Languages : en Pages : 200
Book Description
This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. In addition, it details some interesting applications of the general theory of vortices, such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics.
Author: Andreas Knauf Publisher: Springer ISBN: 3662557746 Category : Science Languages : en Pages : 683
Book Description
As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
Author: Valeriĭ Viktorovich Kozlov
Author: Valeriĭ Viktorovich Kozlov
Author: Jerry B. Marion
Author: V.I. Arnol'd
Author: Robert L. Devaney
Author: National Science Foundation (États-Unis)
Author: J.M. Souriau
Author: Jorge V. José
Author: 
Author: Victor V. Kozlov
Author: Andreas Knauf