Foundations Of Theoretical Mechanics
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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 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 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.
New Foundations For Classical Mechanics
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Author : David Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-09-30
New Foundations For Classical Mechanics written by David Hestenes 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 1999-09-30 with Language Arts & Disciplines categories.
This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces new, coordinate-free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in government and industrial space programs, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion. Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors. Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It contains sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly a hundred pages on relativistic mechanics. The treatment is unique in its exclusive use of geometric algebra and in its detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.
New Foundations For Classical Mechanics
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Author : D. Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Foundations For Classical Mechanics written by D. Hestenes 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 is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
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.
Theoretical Foundations Of Cosmology Introduction To The Global Structure Of Space Time
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Author : Michael Heller
language : en
Publisher: World Scientific
Release Date : 1992-04-15
Theoretical Foundations Of Cosmology Introduction To The Global Structure Of Space Time written by Michael Heller and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-15 with Science categories.
The book's principal aim is to clarify fundamental concepts, decipher mathematical structures used to model space-time and relativistic worlds, and to disclose their physical meaning. After each chapter, philosophical implications of the presented material are commented upon.Both special and general theories of relativity are presented in the book with the stress on their global aspects. Although global mathematical methods are extensively used throughout the book, the definitions of new concepts, short comments and examples make reading smooth without the need to consult other textbooks or review papers.
Symbols Pictures And Quantum Reality On The Theoretical Foundations Of The Physical Universe
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Author : Wolfram Schommers
language : en
Publisher: World Scientific
Release Date : 1995-02-14
Symbols Pictures And Quantum Reality On The Theoretical Foundations Of The Physical Universe written by Wolfram Schommers and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-14 with Science categories.
Information about the reality outside flow via our sense organs into the body, and the brain forms a picture of reality. It is argued that the symbols in the picture have in general no similarity with the objects in the outside world, and many facts support such a view. This conception is discussed in connection with quantum reality. In particular, the role of space and time within quantum theory is also investigated from the historical point of view, highlighting the original ideas. New aspects are covered in connection with the particle concept, particle-wave dualism, locality, the time operator, the superposition principle, and the role of the observer.
Foundations Of Quantum Theory
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Author : E.M. Rasel
language : en
Publisher: IOS Press
Release Date : 2019-01-23
Foundations Of Quantum Theory written by E.M. Rasel and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-23 with Science categories.
This volume provides a summary of the lectures presented at the International School of Physics "Enrico Fermi" on the Foundations of Quantum Theory, organized by the Italian Physical Society in Varenna, Italy from 8-13 July 2016, in collaboration with the Wilhelm und Else Heraeus-Stiftung. It was the first "Enrico Fermi" Summer School on this topic since 1977. Its main goal was to provide an overview of the recent theoretical and experimental developments in an active field of research, the foundations of quantum mechanics. The field is characterized by a dichotomy of unparalleled agreement between theory and experiment on the one hand, and an enormous variety of interpretations of the underlying mathematical formalism on the other hand. This proceedings of the "Enrico Fermi" Summer School of July 2016 contains 21 contributions on a range of topics: the history and interpretations of quantum theory; the principle of complementarity and wave-particle duality; quantum theory from first principles; the reality of the wave function; the concept of the photon; measurement in quantum theory; the interface of quantum theory and general relativity; and quantum optical tests of quantum theory.
Foundations Of Mechanics
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Author : Ralph Abraham
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Foundations Of Mechanics written by Ralph Abraham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
A reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics. It offers a treatment of geometric mechanics. It is also suitable as a textbook for the foundations of differentiable and Hamiltonian dynamics.