Jacobi Dynamics
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Jacobi Dynamics
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Author : V.I. Ferronsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Jacobi Dynamics written by V.I. Ferronsky 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 Science categories.
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.
Jacobi Dynamics
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Author : V.I. Ferronsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-11
Jacobi Dynamics written by V.I. Ferronsky 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 2011-04-11 with Science categories.
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.
Jacobi S Lectures On Dynamics
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Author : A. Clebsch
language : en
Publisher: Springer
Release Date : 2009-08-15
Jacobi S Lectures On Dynamics written by A. Clebsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-15 with Mathematics categories.
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.
Jacobi S Lectures On Dynamics
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Author : Carl Gustav Jakob Jacobi
language : en
Publisher:
Release Date : 2009
Jacobi S Lectures On Dynamics written by Carl Gustav Jakob Jacobi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Dynamics Of The Earth
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Author : V. I. Ferronsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-28
Dynamics Of The Earth written by V. I. Ferronsky 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 2010-06-28 with Science categories.
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.
Variational Principles In Dynamics And Quantum Theory
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Author : Wolfgang Yourgrau
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Variational Principles In Dynamics And Quantum Theory written by Wolfgang Yourgrau and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Science categories.
DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div
Hamiltonian Dynamics
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Author : Gaetano Vilasi
language : en
Publisher: World Scientific
Release Date : 2001
Hamiltonian Dynamics written by Gaetano Vilasi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Dynamics Of The Earth
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Author : V. I. Ferronsky
language : en
Publisher:
Release Date : 2010-11-20
Dynamics Of The Earth written by V. I. Ferronsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-20 with categories.
Geometry From Dynamics Classical And Quantum
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Author : José F. Cariñena
language : en
Publisher: Springer
Release Date : 2014-09-23
Geometry From Dynamics Classical And Quantum written by José F. Cariñena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Science categories.
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
Classical Dynamics
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Author : Donald T. Greenwood
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Classical Dynamics written by Donald T. Greenwood and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Science categories.
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.