Damped Oscillations Of Linear Systems
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Author | : Krešimir Veselić |
Publisher | : Springer |
Total Pages | : 215 |
Release | : 2011-07-09 |
Genre | : Mathematics |
ISBN | : 3642213359 |
The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.
Author | : Krešimir Veselić |
Publisher | : Springer Science & Business Media |
Total Pages | : 215 |
Release | : 2011-07-09 |
Genre | : Language Arts & Disciplines |
ISBN | : 3642213340 |
The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.
Author | : I︠A︡kov Gilelevich Panovko |
Publisher | : |
Total Pages | : 436 |
Release | : 1973 |
Genre | : Elastic solids |
ISBN | : |
Problems such as jumps in elastic systems, problems of aeroelasticity, problems of frictional self-oscillations, and self-synchronization are discussed. The stability of equilibrium shapes of elastic systems is examined. Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces.
Author | : Zoran Vukic |
Publisher | : CRC Press |
Total Pages | : 405 |
Release | : 2003-02-04 |
Genre | : Technology & Engineering |
ISBN | : 0824747631 |
This text emphasizes classical methods and presents essential analytical tools and strategies for the construction and development of improved design methods in nonlinear control. It offers engineering procedures for the frequency domain, as well as solved examples for clear understanding of control applications in the industrial, electrical, process, manufacturing, and automotive industries. The authors discuss Properties of nonlinear systems, stability, linearization methods, operating modes and dynamic analysis methods, phase trajectories in dynamic analysis of nonlinear systems, and harmonic linearization in dynamic analysis of nonlinear control systems operating in stabilization mode.
Author | : Jiri Lebl |
Publisher | : |
Total Pages | : 468 |
Release | : 2019-11-13 |
Genre | : |
ISBN | : 9781706230236 |
Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.
Author | : Douglas Cline |
Publisher | : |
Total Pages | : |
Release | : 2018-08 |
Genre | : |
ISBN | : 9780998837277 |
Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.
Author | : Sondipon Adhikari |
Publisher | : John Wiley & Sons |
Total Pages | : 373 |
Release | : 2013-11-25 |
Genre | : Technology & Engineering |
ISBN | : 1848215215 |
Since Lord Rayleigh introduced the idea of viscous damping in his classic work "The Theory of Sound" in 1877, it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering. However, in the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping. Over the past decade, extensive research has been undertaken on more general "non-viscous" damping models and vibration of non-viscously damped systems. This book, along with a related book Structural Dynamic Analysis with Generalized Damping Models: Identification, is the first comprehensive study to cover vibration problems with general non-viscous damping. The author draws on his considerable research experience to produce a text covering: dynamics of viscously damped systems; non-viscously damped single- and multi-degree of freedom systems; linear systems with non-local and non-viscous damping; reduced computational methods for damped systems; and finally a method for dealing with general asymmetric systems. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Contents 1. Introduction to Damping Models and Analysis Methods. 2. Dynamics of Undamped and Viscously Damped Systems. 3. Non-Viscously Damped Single-Degree-of-Freedom Systems. 4. Non-viscously Damped Multiple-Degree-of-Freedom Systems. 5. Linear Systems with General Non-Viscous Damping. 6. Reduced Computational Methods for Damped Systems
Author | : |
Publisher | : |
Total Pages | : 912 |
Release | : 1976 |
Genre | : Science |
ISBN | : |
Author | : Ian P. Howard |
Publisher | : Oxford University Press |
Total Pages | : 671 |
Release | : 2012-01-27 |
Genre | : Psychology |
ISBN | : 0199877343 |
The three-volume work Perceiving in Depth is a sequel to Binocular Vision and Stereopsis and to Seeing in Depth, both by Ian P. Howard and Brian J. Rogers. This work is much broader in scope than the previous books and includes mechanisms of depth perception by all senses, including aural, electrosensory organs, and the somatosensory system. Volume 1 reviews sensory coding, psychophysical and analytic procedures, and basic visual mechanisms. Volume 2 reviews stereoscopic vision. Volume 3 reviews all mechanisms of depth perception other than stereoscopic vision. The three volumes are extensively illustrated and referenced and provide the most detailed review of all aspects of perceiving the three-dimensional world. Volume 1 starts with a review of the history of visual science from the ancient Greeks to the early 20th century with special attention devoted to the discovery of the principles of perspective and stereoscopic vision. The first chapter also contains an account of early visual display systems, such as panoramas and peepshows, and the development of stereoscopes and stereophotography. A chapter on the psychophysical and analytic procedures used in investigations of depth perception is followed by a chapter on sensory coding and the geometry of visual space. An account of the structure and physiology of the primate visual system proceeds from the eye through the LGN to the visual cortex and higher visual centers. This is followed by a review of the evolution of visual systems and of the development of the mammalian visual system in the embryonic and post-natal periods, with an emphasis on experience-dependent neural plasticity. An account of the development of perceptual functions, especially depth perception, is followed by a review of the effects of early visual deprivation during the critical period of neural plasticity on amblyopia and other defects in depth perception. Volume 1 ends with accounts of the accommodation mechanism of the human eye and vergence eye movements.
Author | : Russell L. Herman |
Publisher | : CRC Press |
Total Pages | : 776 |
Release | : 2013-12-04 |
Genre | : Mathematics |
ISBN | : 146658467X |
Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions