Foundations Of Theoretical Mechanics I

Author : Ruggero Maria Santilli
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 45,5 Mb
Release : 2013-11-21
Category : Science
ISBN : 9783662257715

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Foundations of Theoretical Mechanics I by Ruggero Maria Santilli Pdf

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.

Author : Ruggero Maria Santilli
Publisher : Springer
Page : 296 pages
File Size : 46,5 Mb
Release : 1978
Category : Mathematics
ISBN : UCSD:31822001339050

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Foundations of Theoretical Mechanics by Ruggero Maria Santilli Pdf

Author : Ruggero Maria Santilli
Publisher : Unknown
Page : 392 pages
File Size : 48,9 Mb
Release : 1982-12-01
Category : Electronic
ISBN : 3642867618

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Foundations of Theoretical Mechanics II by Ruggero Maria Santilli Pdf

Author : P. C. Deshmukh
Publisher : Cambridge University Press
Page : 591 pages
File Size : 44,7 Mb
Release : 2019-12-12
Category : Mathematics
ISBN : 9781108480567

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Foundations of Classical Mechanics by P. C. Deshmukh Pdf

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

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400948020

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New Foundations for Classical Mechanics by D. Hestenes Pdf

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.

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 44,7 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471223

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New Foundations for Classical Mechanics by D. Hestenes Pdf

(revised) 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 applications 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.

Author : Belal E. Baaquie
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 45,5 Mb
Release : 2013-01-26
Category : Science
ISBN : 9781461462248

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The Theoretical Foundations of Quantum Mechanics by Belal E. Baaquie Pdf

The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and assumes introductory knowledge of quantum mechanics. Its objective is to provide a solid foundation for the reader to reach a deeper understanding of the principles of quantum mechanics.

Author : W. Noll
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642658174

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The Foundations of Mechanics and Thermodynamics by W. Noll Pdf

German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.

Author : Ralph Abraham
Publisher : CRC Press
Page : 849 pages
File Size : 45,5 Mb
Release : 2019-04-24
Category : Science
ISBN : 9780429689048

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Foundations Of Mechanics by Ralph Abraham Pdf

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

Author : R. Jancel
Publisher : Elsevier
Page : 440 pages
File Size : 42,9 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483186269

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Foundations of Classical and Quantum Statistical Mechanics by R. Jancel Pdf

Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.

Author : Nikolai Nikolaevich Polyakhov,Mikhail Petrovich Yushkov,Sergey Andreevich Zegzhda
Publisher : Springer Nature
Page : 526 pages
File Size : 51,8 Mb
Release : 2021-08-30
Category : Technology & Engineering
ISBN : 9783030640613

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Rational and Applied Mechanics by Nikolai Nikolaevich Polyakhov,Mikhail Petrovich Yushkov,Sergey Andreevich Zegzhda Pdf

Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). This first volume of the textbook contains the parts “Kinematics” and “Dynamics”. The part “Kinematics” presents in detail the theory of curvilinear coordinates which is actively used in the part “Dynamics”, in particular, in the theory of constrained motion and variational principles in mechanics. For describing the motion of a system of particles, the notion of a Hertz representative point is used, and the notion of a tangent space is applied to investigate the motion of arbitrary mechanical systems. In the final chapters Hamilton-Jacobi theory is applied​ for the integration of equations of motion, and the elements of special relativity theory are presented. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.

Author : Michael Spivak
Publisher : Unknown
Page : 733 pages
File Size : 42,9 Mb
Release : 2010
Category : Mechanics
ISBN : 0914098322

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Physics for Mathematicians by Michael Spivak Pdf

Author : Sol Wieder
Publisher : Elsevier
Page : 416 pages
File Size : 52,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323141710

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The Foundations of Quantum Theory by Sol Wieder Pdf

The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. The book is organized into three parts encompassing 12 chapters that cover topics on one-and many-particle systems and relativistic quantum mechanics and field theory. The first part of the book discusses the developments that formed the basis for the old quantum theory and the use of classical mechanics to develop the theory of quantum mechanics. This part includes considerable chapters on the formal theory of quantum mechanics and the wave mechanics in one- and three-dimension, with an emphasis on Coulomb problem or the hydrogen atom. The second part deals with the interacting particles and noninteracting indistinguishable particles and the material covered is fundamental to almost all branches of physics. The third part presents the pertinent equations used to illustrate the relativistic quantum mechanics and quantum field theory. This book is of value to undergraduate physics students and to students who have background in mechanics, electricity and magnetism, and modern physics.

Author : Travis Norsen
Publisher : Springer
Page : 310 pages
File Size : 42,8 Mb
Release : 2017-08-17
Category : Science
ISBN : 9783319658674

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Foundations of Quantum Mechanics by Travis Norsen Pdf

Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study.

Author : Stanislaw Bazanski
Publisher : Elsevier
Page : 614 pages
File Size : 50,7 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483291611

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Foundations of Mechanics by Stanislaw Bazanski Pdf

In the last three decades the field of mechanics has seen spectacular progress due to the demand for applications in problems of cosmology, thermonuclear fusion, metallurgy, etc. This book provides a broad and thorough overview on the foundations of mechanics. It discusses theoretical mechanics and continuum mechanics, as well as phenomenological thermodynamics, quantum mechanics and relativistic mechanics. Each chapter presents the basic physical facts of interest without going into details and derivations and without using advanced mathematical formalism. The first part constitutes a classical exposition of Lagrange's and Hamilton's analytical mechanics on which most of the continuum theory is based. The section on continuum mechanics focuses mainly on the axiomatic foundations, with many pointers for further research in this area. Special attention is given to modern continuum thermodynamics, both for the foundations and applications. A section on quantum mechanics is also included, since the phenomenological description of various quantum phenomena is becoming of increasing importance. The work will prove indispensable to engineers wishing to keep abreast of recent theoretical advances in their field, as well as initiating and guiding future research.