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Jacobi Dynamics
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Download or read book Jacobi Dynamics written by V.I. Ferronsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets forth and builds upon the fundamentals of the dynamics of natural systems in formulating the problem presented by Jacobi in his famous lecture series "Vorlesungen tiber Dynamik" (Jacobi, 1884). In the dynamics of systems described by models of discrete and continuous media, the many-body problem is usually solved in some approximation, or the behaviour of the medium is studied at each point of the space it occupies. Such an approach requires the system of equations of motion to be written in terms of space co-ordinates and velocities, in which case the requirements of an internal observer for a detailed description of the processes are satisfied. In the dynamics discussed here we study the time behaviour of the fundamental integral characteristics of the physical system, i. e. the Jacobi function (moment of inertia) and energy (potential, kinetic and total), which are functions of mass density distribution, and the structure of a system. This approach satisfies the requirements of an external observer. It is designed to solve the problem of global dynamics and the evolution of natural systems in which the motion of the system's individual elements written in space co-ordinates and velocities is of no interest. It is important to note that an integral approach is made to internal and external interactions of a system which results in radiation and absorption of energy. This effect constitutes the basic physical content of global dynamics and the evolution of natural systems.
Book Synopsis Jacobi's Lectures on Dynamics by : A. Clebsch
Download or read book Jacobi's Lectures on Dynamics written by A. Clebsch and published by Springer. This book was released on 2009-08-15 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name of C. G. J. Jacobi is familiar to every student of mathematics, thanks to the Jacobion determinant, the Hamilton-Jacobi equations in dynamics, and the Jacobi identity for vector fields. Best known for his contributions to the theory of elliptic and abelian functions, Jacobi is also known for his innovative teaching methods and for running the first research seminar in pure mathematics. A record of his lectures on Dynamics given in 1842-43 at Konigsberg, edited by A. Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters.
Download or read book Jacobi Dynamics written by V.I. Ferronsky and published by Springer Science & Business Media. This book was released on 2011-04-11 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their approach to Earth dynamics the authors consider the fundamentals of Jacobi Dynamics (1987, Reidel) for two reasons. First, because satellite observations have proved that the Earth does not stay in hydrostatic equilibrium, which is the physical basis of today’s treatment of geodynamics. And secondly, because satellite data have revealed a relationship between gravitational moments and the potential of the Earth’s outer force field (potential energy), which is the basis of Jacobi Dynamics. This has also enabled the authors to come back to the derivation of the classical virial theorem and, after introducing the volumetric forces and moments, to obtain a generalized virial theorem in the form of Jacobi’s equation. Thus a physical explanation and rigorous solution was found for the famous Jacobi’s equation, where the measure of the matter interaction is the energy. The main dynamical effects which become understandable by that solution can be summarized as follows: • the kinetic energy of oscillation of the interacting particles which explains the physical meaning and nature of the gravitation forces; • separation of the shell’s rotation of a self-gravitating body with respect to the mass density; difference in angular velocities of the shell rotation; • continuity in changing the potential of the outer gravitational force field together with changes in density distribution of the interacting masses (volumetric center of masses); • the nature of the precession of the Earth, the Moon and satellites; the nature of the rotating body’s magnetic field and the generation of the planet’s electromagnetic field. As a final result, the creation of the bodies in the Solar System having different orbits was discussed. This result is based on the discovery that all the averaged orbital velocities of the bodies in the Solar System and the Sun itself are equal to the first cosmic velocities of their proto-parents during the evolution of their redistributed mass density. Audience The work is a logical continuation of the book Jacobi Dynamics and is intended for researchers, teachers and students engaged in theoretical and experimental research in various branches of astronomy (astrophysics, celestial mechanics and stellar dynamics and radiophysics), geophysics (physics and dynamics of the Earth’s body, atmosphere and oceans), planetology and cosmogony, and for students of celestial, statistical, quantum and relativistic mechanics and hydrodynamics.
Book Synopsis Dynamics of the Earth by : V. I. Ferronsky
Download or read book Dynamics of the Earth written by V. I. Ferronsky and published by Springer Science & Business Media. This book was released on 2010-06-28 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their search for solutions to problems concerning the dynamics of the Earth as a self-gravitating body, the authors have applied the fundamentals found in their book “Jacobi Dynamics” (1987, Reidel). First, satellite observations have shown that the Earth does not remain in hydrostatic equilibrium, which forms the physical basis of modern geodynamics. Secondly, satellite data have established a relationship between the planet’s polar moment of inertia and the potential of the Earth’s outer force field, which proves the most basic point of Jacobi dynamics. This allowed the authors to revise their derivation of the classical virial theorem, introducing the concept of a volumetric force and volumetric moment, and so to obtain a generalized virial theorem in the form of Jacobi’s equation. The main dynamical effects are: the kinetic energy of oscillation of the interacting particles, which explains the physical meaning and nature of gravitational forces; separation of shells of a self-gravitating body with respect to its mass density; differences in angular velocities of the shell’s rotation; continuity in variance of the potential of the outer gravitational force field, together with reductions in the envelope of the interacting masses (volumetric center of gravity); the nature of Earth, Moon and satellite precession; the nature and generating mechanism of the planet’s electromagnetic field; the common nature of gravitational and electromagnetic energy, and other related issues. The work is a logical continuation of the book "Jacobi Dynamics" and is intended for researchers, teachers and students engaged in theoretical and experimental research in various branches of astronomy, geophysics, planetology and cosmogony, and for students of celestial, statistical, quantum and relativistic mechanics and hydrodynamics.
Book Synopsis Classical Dynamics and Its Quantum Analogues by : David Park
Download or read book Classical Dynamics and Its Quantum Analogues written by David Park and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The short Heroic Age of physics that started in 1925 was one of the rare occasions when a deep consideration of the question: What does physics really say? was necessary in carrying out numerical calculations. In many parts of microphysics the calculations have now become relatively straightforward if not easy, but most physicists seem to agree that some questions of principle remain to be resolved, even if they do not think it is very important to do so. This situation has affected the way people think and write about quantum mechanics, a gingerly approach to fundamentals and a tendency to emphasize what fifty years ago was new in the new theory at the expense of continuity with what came before it. Nowadays those who look into the subject are more likely to be struck by unexpected similarities between quantum and classical mechanics than by dramatic contrasts they had been led to expect. It is often said that the hardest part of understanding quantum mechanics is to understand that there is nothing to understand; all the same, to think quantum mechanically it helps to have firm mental connections with classical physics and to know exactly what these connections do and do not imply. This book originated more than a decade ago as informal lecture notes [OP, prepared for use in a course taught from time to time to advanced undergraduates at Williams College.
Book Synopsis Gravitation, Inertia and Weightlessness by : V.I. Ferronsky
Download or read book Gravitation, Inertia and Weightlessness written by V.I. Ferronsky and published by Springer. This book was released on 2016-04-25 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work discusses the problem of physical meaning of the three main dynamical properties of matter motion, namely gravitation, inertia and weightlessness. It considers that Newtonian gravitation and Galileo’s inertia are the centrifugal effects of interaction energy of a self-gravitating n-body system and its potential field. A self-gravitating celestial body appears to be an excellent natural centrifuge that is rotated by the energy of interacting elementary particles. Weightlessness is a consequence of the centrifugal effect of elementary particles interaction that appears at differentiation of a body matter with respect to density. The author analyzes the problem of creation of mass particles and elements from the elementary particles of “dark matter”, and discusses the basic physics of the Jacobi dynamics from the viewpoint of quantum gravitation. Chapters assert that the fundamentals of Jacobi dynamics completely correspond to conditions of natural centrifuges. The centrifuge is an excellent experimental model for the study of dynamical effects in solving the many body problem. In this book, readers may follow the demonstration of some of those studies and follow derivations, solutions and conclusions that provide a solid basis for further research in celestial mechanics, geophysics, astrophysics, geo- and planetary sciences.
Book Synopsis Universal Concept of Complexity by the Dynamic Redundance Paradigm by : Andrei P. Kirilyuk
Download or read book Universal Concept of Complexity by the Dynamic Redundance Paradigm written by Andrei P. Kirilyuk and published by . This book was released on 1997 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations by : M.D.S. Aliyu
Download or read book Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations written by M.D.S. Aliyu and published by CRC Press. This book was released on 2017-12-19 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.
Book Synopsis Elements of Analytical Dynamics by : Rudolph Kurth
Download or read book Elements of Analytical Dynamics written by Rudolph Kurth and published by Elsevier. This book was released on 2014-07-10 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Analytical Dynamics deals with dynamics, which studies the relationship between motion of material bodies and the forces acting on them. This book is a compilation of lectures given by the author at the Georgia and Institute of Technology and formed a part of a course in Topological Dynamics. The book begins by discussing the notions of space and time and their basic properties. It then discusses the Hamilton-Jacobi theory and Hamilton's principle and first integrals. The text concludes with a discussion on Jacobi's geometric interpretation of conservative systems. This book will be of direct use to graduate students of Mathematics with minimal background in Theoretical Mechanics.
Book Synopsis Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by : Maurizio Falcone
Download or read book Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations written by Maurizio Falcone and published by SIAM. This book was released on 2014-01-31 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.
Book Synopsis Hamiltonian Dynamics by : Gaetano Vilasi
Download or read book Hamiltonian Dynamics written by Gaetano Vilasi and published by World Scientific. This book was released on 2001 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations. Contents: Analytical Mechanics: The Lagrangian Coordinates; Hamiltonian Systems; Transformation Theory; The Integration Methods; Basic Ideas of Differential Geometry: Manifolds and Tangent Spaces; Differential Forms; Integration Theory; Lie Groups and Lie Algebras; Geometry and Physics: Symplectic Manifolds and Hamiltonian Systems; The Orbits Method; Classical Electrodynamics; Integrable Field Theories: KdV Equation; General Structures; Meaning and Existence of Recursion Operators; Miscellanea; Integrability of Fermionic Dynamics. Readership: Physicists and mathematicians.
Book Synopsis Variational Principles in Dynamics and Quantum Theory by : Wolfgang Yourgrau
Download or read book Variational Principles in Dynamics and Quantum Theory written by Wolfgang Yourgrau and published by Courier Corporation. This book was released on 2012-04-26 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div
Book Synopsis Classical Dynamics by : Donald T. Greenwood
Download or read book Classical Dynamics written by Donald T. Greenwood and published by Courier Corporation. This book was released on 2012-05-04 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text provides strong background in more abstract areas of dynamical theory. Hamilton's equations, d'Alembert's principle, Hamilton-Jacobi theory, other topics. Problems and references. 1977 edition.
Book Synopsis Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes by :
Download or read book Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes written by and published by . This book was released on 1986 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Selected Papers on Wave Mechanics by : Louis de Broglie
Download or read book Selected Papers on Wave Mechanics written by Louis de Broglie and published by . This book was released on 1928 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Waves in Neural Media by : Paul C. Bressloff
Download or read book Waves in Neural Media written by Paul C. Bressloff and published by Springer Science & Business Media. This book was released on 2013-10-17 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations. Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations or partial differential equations, making this an accessible and unique contribution to the field of mathematical biology.
Book Synopsis Jacobi's Lectures on Dynamics by : Carl Gustav Jakob Jacobi
Download or read book Jacobi's Lectures on Dynamics written by Carl Gustav Jakob Jacobi and published by . This book was released on 2009 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt:
