Foundations Of Theoretical Mechanics I

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Foundations Of Theoretical Mechanics I

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Author : Ruggero Maria Santilli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Foundations Of Theoretical Mechanics I written by Ruggero Maria Santilli 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 2013-11-21 with Science categories.

The objective of this monograph is to present some methodological foundations of theoretical mechanics that are recommendable to graduate students prior to, or jointly with, the study of more advanced topics such as statistical mechanics, thermodynamics, and elementary particle physics. A program of this nature is inevitably centered on the methodological foundations for Newtonian systems, with particular reference to the central equations of our theories, that is, Lagrange's and Hamilton's equations. This program, realized through a study of the analytic representations in terms of Lagrange's and Hamilton's equations of generally nonconservative Newtonian systems (namely, systems with Newtonian forces not necessarily derivable from a potential function), falls within the context of the so-called Inverse Problem, and consists of three major aspects: l. The study of the necessary and sufficient conditions for the existence of a Lagrangian or Hamiltonian representation of given equations of motion with arbitrary forces; 2. The identification of the methods for the construction of a Lagrangian or Hamiltonian from given equations of motion verifying conditions 1; and 3 The analysis of the significance of the underlying methodology for other aspects of Newtonian Mechanics, e. g. , transformation theory, symmetries, and first integrals for nonconservative Newtonian systems. This first volume is devoted to the foundations of the Inverse Problem, with particular reference to aspects I and 2.

Foundations Of Theoretical Mechanics

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Author : Ruggero Maria Santilli
language : en
Publisher: Springer
Release Date : 1978

Foundations Of Theoretical Mechanics written by Ruggero Maria Santilli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.

Foundations Of Theoretical Mechanics Ii

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Author : Ruggero Maria Santilli
language : en
Publisher: Springer
Release Date : 2012-04-09

Foundations Of Theoretical Mechanics Ii written by Ruggero Maria Santilli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-09 with Science categories.

In the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order.

Foundations Of Classical Mechanics

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Author : P. C. Deshmukh
language : en
Publisher: Cambridge University Press
Release Date : 2019-12-12

Foundations Of Classical Mechanics written by P. C. Deshmukh and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-12 with Mathematics categories.

The book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.

Foundations Of Quantum Mechanics I

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Author : G. Ludwig
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Foundations Of Quantum Mechanics I written by G. Ludwig 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 is the first volume of a two-volume work on the Foundations of Quantum Mechanics, and is intended as a new edition of the author's book Die Grundlagen der Quantenmechanik [37] which was published in 1954. In this two-volume work we will seek to obtain an improved formulation of the interpretation of quantum mechanics based on experiments. The second volume will appear shortly. Since the publication of [37] there have been several attempts to develop a basis for quantum mechanics which is, in the large part, based upon the work of J. von Neumann [38]. In particular, we mention the books ofG. W. Mackey [39], J. Jauch [40], C. Piron [41], M. Drieschner [9], and the original work ofS. P. Gudder [42], D.J. Foulis and C.H. Randall [43], and N. Zierler [44]. Here we do not seek to compare these different formulations of the foundations of quantum mechanics. We refer interested readers to [45] for such comparisons.

Relativistic Classical Mechanics And Electrodynamics

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Author : Martin Land
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

Relativistic Classical Mechanics And Electrodynamics written by Martin Land and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.

This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter to play the role of Newton's universal and monotonically advancing time. Fundamental physics is described by the -evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five -dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at to an infinitesimally close 4D block universe defined at +. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory.

Foundations Of Classical And Quantum Electrodynamics

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Author : Igor N. Toptygin
language : en
Publisher: John Wiley & Sons
Release Date : 2013-12-30

Foundations Of Classical And Quantum Electrodynamics written by Igor N. Toptygin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-30 with Science categories.

This advanced textbook covers many fundamental, traditional and new branches of electrodynamics, as well as the related fields of special relativity, quantum mechanics and quantum electrodynamics. The book introduces the material at different levels, oriented towards 3rd-4th year bachelor, master, and PhD students. This is so as to describe the whole complexity of physical phenomena, instead of a mosaic of disconnected data. The required mathematical background is collated in Chapter 1, while the necessary physical background is included in the main text of the corresponding chapters and also given in appendices. The content is based on teaching material tested on students over many years, and their training to apply general theory for solving scientific and engineering problems. To this aim, the book contains approximately 800 examples and problems, many of which are described in detail. Some of these problems are designed for students to work on their own with only the answers and descriptions of results, and may be solved selectively. The examples are key ingredients to the theoretical course; the user should study all of them while reading the corresponding chapters. Equally suitable as a reference for researchers specialized in science and engineering.

Origins

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Author : Karl H. Pribram
language : en
Publisher: Routledge
Release Date : 2018-10-24

Origins written by Karl H. Pribram and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Psychology categories.

The result of the second Appalachian conference on neurodynamics, this volume focuses on the problem of "order," its origins, evolution, and future. Central to this concern lies our understanding of time. Both classical and quantum physics have developed their conceptions within a framework of time symmetry. Divided into four major sections, this book: * provides refreshingly new approaches to the problem of the evolution of order, indicating the directions that need to be taken in subsequent conferences which will address learning and memory more directly; * addresses the issue of how information becomes transmitted in the nervous system; * shows how patterns are constructed at the synaptodendritic level of processing and how such pattern construction relates to image processing; and * deals with the control operations which operate on image processing to construct entities such as visual and auditory objects such as phonemes. The aim of the conference was to bring together professionals to exchange ideas -- some were fairly worked out; others were in their infancy. As a result, one of the most valuable aspects of the conference is that it fostered lasting interactive relationships among these leading researchers.

Mathematical Essays On Growth And The Emergence Of Form

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Author : Peter L. Antonelli
language : en
Publisher: University of Alberta
Release Date : 1985

Mathematical Essays On Growth And The Emergence Of Form written by Peter L. Antonelli and has been published by University of Alberta this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

Of interest to theoretical biologists, as well as mathematicians, physical scientists or anyone concerned with problems in growth, chemical ecology and the developmental biology of form, these essays on biological modelling by American, British and Canadian researchers provide an interesting geometric excursion to the frontiers of contemporary mathematical biology.

Quantum Theory And The Schism In Physics

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Author : Karl Popper
language : en
Publisher: Routledge
Release Date : 2013-04-15

Quantum Theory And The Schism In Physics written by Karl Popper and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Philosophy categories.

Quantum Theory and the Schism in Physics is one of the three volumes of Karl Popper’s Postscript to the Logic of scientific Discovery. The Postscript is the culmination of Popper’s work in the philosophy of physics and a new famous attack on subjectivist approaches to philosophy of science. Quantum Theory and the Schism in Physics is the third volume of the Postscript. It may be read independently, but it also forms part of Popper’s interconnected argument in the Postscript. It presents Popper’s classic statement on quantum physics and offers important insights into his thinking on problems of method within science and physics as a whole.