Foundations of Theoretical Mechanics I
Foundations of Theoretical Mechanics I

Author: Ruggero Maria Santilli

Publisher: Springer

Published: 1984-01-01

Total Pages: 266

ISBN-13: 9783662236833

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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 Classical Mechanics
Foundations of Classical Mechanics

Author: P. C. Deshmukh

Publisher: Cambridge University Press

Published: 2019-12-12

Total Pages: 591

ISBN-13: 110848056X

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

New Foundations for Classical Mechanics
New Foundations for Classical Mechanics

Author: D. Hestenes

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 655

ISBN-13: 9400948026

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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.

New Foundations for Classical Mechanics
New Foundations for Classical Mechanics

Author: D. Hestenes

Publisher: Springer Science & Business Media

Published: 2005-12-17

Total Pages: 716

ISBN-13: 0306471221

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(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.

Foundations Of Mechanics
Foundations Of Mechanics

Author: Ralph Abraham

Publisher: CRC Press

Published: 2019-04-24

Total Pages: 849

ISBN-13: 0429689047

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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.

Quantum Mechanics II
Quantum Mechanics II

Author: Rubin H. Landau

Publisher: John Wiley & Sons

Published: 2008-07-11

Total Pages: 519

ISBN-13: 3527617442

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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.

Foundations of Theoretical Mechanics I
Foundations of Theoretical Mechanics I

Author: Ruggero Maria Santilli

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 282

ISBN-13: 3662257718

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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.

An Elementary Treatise on Theoretical Mechanics
An Elementary Treatise on Theoretical Mechanics

Author: Sir James H. Jeans

Publisher: Courier Corporation

Published: 2013-05-23

Total Pages: 381

ISBN-13: 0486174697

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In 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.