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Author: P. C. Deshmukh
Publisher: Cambridge University Press
Published: 2019-12-12
Total Pages: 591
ISBN-13: 110848056X
DOWNLOAD EBOOKThe book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.
Author: Ruggero Maria Santilli
Publisher: Springer
Published: 1984-01-01
Total Pages: 266
ISBN-13: 9783662236833
DOWNLOAD EBOOKThe 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
Published: 1978
Total Pages: 296
ISBN-13:
DOWNLOAD EBOOKAuthor: D. Hestenes
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 655
ISBN-13: 9400948026
DOWNLOAD EBOOKThis 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: Ruggero Maria Santilli
Publisher: Springer Science & Business Media
Published: 2013-11-21
Total Pages: 282
ISBN-13: 3662257718
DOWNLOAD EBOOKThe 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: Ralph Abraham
Publisher: CRC Press
Published: 2019-04-24
Total Pages: 849
ISBN-13: 0429689047
DOWNLOAD EBOOKFoundations 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: Ruggero Maria Santilli
Publisher:
Published: 1982-12-01
Total Pages: 392
ISBN-13: 9783642867613
DOWNLOAD EBOOKAuthor: Belal E. Baaquie
Publisher: Springer Science & Business Media
Published: 2013-01-26
Total Pages: 274
ISBN-13: 146146224X
DOWNLOAD EBOOKThe 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: Sir James H. Jeans
Publisher: Courier Corporation
Published: 2013-05-23
Total Pages: 381
ISBN-13: 0486174697
DOWNLOAD EBOOKIn addition to being among the twentieth century’s major scientific figures, Sir James Jeans (1877–1946) was also one of the greatest modern science expositors. His classic introduction to mechanics endures as a clear and concise presentation of first principles. Although brief, it encompasses a remarkably wide selection of topics. Its subjects include rest and motion, force and the laws of motion, forces acting on a single particle, statics of systems of particles, statics of rigid bodies, center of gravity, work, motion of a particle under constant forces, motion of systems of particles, motion of a particle under a variable force, motion of rigid bodies, and generalized coordinates. Within each chapter, the author carefully explains the most elementary concepts (such as velocity, acceleration, Newton’s laws, friction, moments, and kinetic energy), and he illustrates them with examples. Ideal for beginning physics students or for more advanced readers in need of refreshment, the text emphasizes the fundamental physical principles rather than mathematics or applications. So clearly written that it can be read and understood outside the classroom, it features hundreds of fully worked illustrative examples and test exercises.
Author: R. Jancel
Publisher: Elsevier
Published: 2013-10-22
Total Pages: 441
ISBN-13: 1483186261
DOWNLOAD EBOOKFoundations 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.
