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Author : Ruggero Maria Santilli
Publisher : Unknown
Page : 392 pages
File Size : 49,8 Mb
Release : 1982-12-01
Category : Electronic
ISBN : 3642867618
Author : Ruggero Maria Santilli
Publisher : Springer
Page : 266 pages
File Size : 45,5 Mb
Release : 1984-01-01
Category : Science
ISBN : 3662236834
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 : 55,9 Mb
Release : 1978
Category : Mathematics
ISBN : UCSD:31822001339050
Author : Ruggero Maria Santilli
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 55,6 Mb
Release : 2013-11-21
Category : Science
ISBN : 9783662257715
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 : P. C. Deshmukh
Publisher : Cambridge University Press
Page : 591 pages
File Size : 51,6 Mb
Release : 2019-12-12
Category : Mathematics
ISBN : 9781108480567
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 : 51,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400948020
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 : 40,5 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471223
(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 : Rubin H. Landau
Publisher : John Wiley & Sons
Page : 519 pages
File Size : 40,9 Mb
Release : 2008-07-11
Category : Science
ISBN : 9783527617449
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature. As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists.
Author : Nikolai Nikolaevich Polyakhov,Mikhail Petrovich Yushkov,Sergey Andreevich Zegzhda
Publisher : Springer Nature
Page : 526 pages
File Size : 53,9 Mb
Release : 2021-08-30
Category : Technology & Engineering
ISBN : 9783030640613
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 : Belal E. Baaquie
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 47,7 Mb
Release : 2013-01-26
Category : Science
ISBN : 9781461462248
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 : Ralph Abraham
Publisher : CRC Press
Page : 849 pages
File Size : 46,9 Mb
Release : 2019-04-24
Category : Science
ISBN : 9780429689048
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 : J.T. Oden,J.N. Reddy
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642688119
This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. We also gratefully acknowedge that much of our own research work on va ri at i ona 1 theory was supported by the U. S. Ai r Force Offi ce of Scientific Research. We are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and painstaking job of typing the manuscript. This revised edition contains only minor revisions of the first. Some misprints and errors have been corrected, and some sections were deleted, which were felt to be out of date.
Author : R. Jancel
Publisher : Elsevier
Page : 441 pages
File Size : 55,9 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483186269
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 : Sol Wieder
Publisher : Elsevier
Page : 416 pages
File Size : 47,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323141710
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 : Günther Ludwig
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 53,6 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662287262
In this second volume on the Foundations of Quantum Mechanics we shall show how it is possible, using the methodology presented in Volume I, to deduce some of the most important applications of quantum mechanics. These deductions are concerned with the structures of the microsystems rather than the technical details of the construction of preparation and registration devices. Accordingly. the only new axioms (relative to Volume I) which are introduced are concerned with the relationship between ensemble operators W, effect operators F, and certain construction principles of the preparation and registration devices. The applications described here are concerned with the measurement of atomic and molecular structure and of collision experiments. An additional and essential step towards a theoretical description of the preparation and registration procedures is carried out in Chapter XVII. Here we demonstrate how microscopic collision processes (that is, processes which can be described by quantum mechanics) can be used to obtain novel preparation and registration procedures if we take for granted the knowledge of only a few macroscopic preparation and registration procedures. By clever use of collision processes we are often able to obtain very precise results for the operators Wand F which describe the total procedures from a very imprecise knowledge of the macroscopic parts of the preparation and regis tration processes. In this regard experimental physicists have done brilliant work. In this sense Chapter XVII represents a general theoretical foundation for the procedures used by experimental physicists.
