Author: van der Burgh (A.H.P.)Publisher:
ISBN:
Category :
Languages : en
Pages : 170
Book Description
Studies in the Asymptotic Theory of Nonlinear Resonance
Author: van der Burgh (A.H.P.)Publisher:
ISBN:
Category :
Languages : en
Pages : 170
Book Description
Studies in the asymptotic theory of nonlinear resonance
Author: Adriaan H. van der BurghPublisher:
ISBN:
Category : Asymptotes
Languages : en
Pages : 170
Book Description
Asymptotic Methods in the Theory of Non-linear Oscillations
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bovPublisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
Book Description
On the Theory of Nonlinear Resonance
Author: Jan A. SandersAveraging Methods in Nonlinear Dynamical Systems
Author: Jan A. SandersPublisher: Springer Science & Business Media
ISBN: 1475745753
Category : Mathematics
Languages : en
Pages : 259
Book Description
In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.
A Toolbox of Averaging Theorems
Author: Ferdinand VerhulstPublisher: Springer Nature
ISBN: 3031345150
Category : Mathematics
Languages : en
Pages : 199
Book Description
This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε. Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs). In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.
Asymptotic Analysis II
Author: F. VerhulstPublisher: Springer
ISBN: 3540396128
Category : Mathematics
Languages : en
Pages : 503
Book Description
Asymptotic Analysis
Author: F. VerhulstPublisher: Springer
ISBN: 3540353321
Category : Mathematics
Languages : en
Pages : 249
Book Description
Mathematical Aspects of Classical and Celestial Mechanics
Author: Vladimir I. ArnoldPublisher: Springer Science & Business Media
ISBN: 3540489266
Category : Mathematics
Languages : en
Pages : 505
Book Description
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.
Problems of the Asymptotic Theory of Nonstationary Vibrations
Author: Юрий Алексеевич МитропольскийPublisher:
ISBN:
Category : Nonlinear systems
Languages : en
Pages : 1234
Book Description