Foundations Of Theoretical Mechanics
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Foundations of Theoretical Mechanics I
Author | : Ruggero Maria Santilli |
Publsiher | : Springer |
Total Pages | : 266 |
Release | : 1984-01-01 |
Genre | : Science |
ISBN | : 3662236834 |
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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 I
Author | : Ruggero Maria Santilli |
Publsiher | : Springer Science & Business Media |
Total Pages | : 282 |
Release | : 2013-11-21 |
Genre | : Science |
ISBN | : 9783662257715 |
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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
Author | : Ruggero Maria Santilli |
Publsiher | : Springer |
Total Pages | : 296 |
Release | : 1978 |
Genre | : Mathematics |
ISBN | : UCSD:31822001339050 |
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Foundations of Classical Mechanics
Author | : P. C. Deshmukh |
Publsiher | : Cambridge University Press |
Total Pages | : 591 |
Release | : 2019-12-12 |
Genre | : Mathematics |
ISBN | : 9781108480567 |
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The book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.
Foundations of Theoretical Mechanics II
Author | : Ruggero Maria Santilli |
Publsiher | : Unknown |
Total Pages | : 392 |
Release | : 1982-12-01 |
Genre | : Electronic Book |
ISBN | : 3642867618 |
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New Foundations for Classical Mechanics
Author | : D. Hestenes |
Publsiher | : Springer Science & Business Media |
Total Pages | : 655 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9789400948020 |
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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.
The Theoretical Foundations of Quantum Mechanics
Author | : Belal E. Baaquie |
Publsiher | : Springer Science & Business Media |
Total Pages | : 274 |
Release | : 2013-01-26 |
Genre | : Science |
ISBN | : 9781461462248 |
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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.
Foundations Of Mechanics
Author | : Ralph Abraham |
Publsiher | : CRC Press |
Total Pages | : 849 |
Release | : 2019-04-24 |
Genre | : Science |
ISBN | : 9780429689048 |
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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.