Classical Mechanics And Dynamical Systems
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Classical Mechanics And Dynamical Systems
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Author : National Science Foundation (États-Unis)
language : en
Publisher:
Release Date : 1981
Classical Mechanics And Dynamical Systems written by National Science Foundation (États-Unis) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Dynamical Systems In Classical Mechanics
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Author : Valeriĭ Viktorovich Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Dynamical Systems In Classical Mechanics written by Valeriĭ Viktorovich Kozlov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Mechanics And Dynamical Systems With Mathematica
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Author : Nicola Bellomo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mechanics And Dynamical Systems With Mathematica written by Nicola Bellomo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa tions is a relevant, maybe the fundamental, aspect of the interactions be tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization.
Classical Mechanics And Dynamical Systems
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Author : Conference Board of the Mathematical Sciences
language : en
Publisher: CRC Press
Release Date : 1981-09-01
Classical Mechanics And Dynamical Systems written by Conference Board of the Mathematical Sciences and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-09-01 with Mathematics categories.
Dynamical Systems In Classical Mechanics
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Author :
language : en
Publisher:
Release Date : 1995
Dynamical Systems In Classical Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Classical Mathematical Physics
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Author : Walter Thirring
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-17
Classical Mathematical Physics written by Walter Thirring and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-17 with Science categories.
This volume combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and pertubation theory. Problems discussed in considerable detail include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differenial geometry throughout, treating both Maxwell's and Einstein's equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds; it concludes by applying these results to the life and death of stars.
Dynamical Systems Iii
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Author : Vladimir I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Dynamical Systems Iii written by Vladimir I. Arnol'd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.
Mathematical Aspects Of Classical And Celestial Mechanics
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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-05
Mathematical Aspects Of Classical And Celestial Mechanics written by Vladimir I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Mathematics categories.
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.
Classical Mechanics And Dynamical Systems
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Author : Robert L. Devaney
language : en
Publisher:
Release Date : 1981
Classical Mechanics And Dynamical Systems written by Robert L. Devaney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Dynamical Systems And Geometric Mechanics
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Author : Jared Maruskin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-21
Dynamical Systems And Geometric Mechanics written by Jared Maruskin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Science categories.
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.