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Fundamental Principles Of Classical Mechanics

Author: Kai S Lam
Publisher: World Scientific Publishing Company
ISBN: 9814551503
Size: 48.87 MB
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This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

Fundamental Principles Of Classical Mechanics

Author: Kai Shue Lam
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814551489
Size: 44.51 MB
Format: PDF, Kindle
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This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

Analytical Mechanics

Author: Nivaldo A. Lemos
Publisher: Cambridge University Press
ISBN: 1108416586
Size: 61.11 MB
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An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

Classical Dynamics

Author: E C G Sudarshan
Publisher: World Scientific Publishing Company
ISBN: 9814713899
Size: 13.59 MB
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Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics. Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of dynamical systems is discussed in detail, and Poisson brackets are developed as a realization of Lie brackets. Other topics include treatments of classical spin, elementary relativistic systems in the classical context, irreducible realizations of the Galileo and Poincaré groups, and hydrodynamics as a Galilean field theory. Students will also find that this approach that deals with problems of manifest covariance, the no-interaction theorem in Hamiltonian mechanics and the structure of action-at-a-distance theories provides all the essential preparatory groundwork for a passage to quantum field theory. This reprinting of the original text published in 1974 is a testimony to the vitality of the contents that has remained relevant over nearly half a century.

Classical Mechanics With Mathematica

Author: Antonio Romano
Publisher: Springer Science & Business Media
ISBN: 0817683518
Size: 39.10 MB
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This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.​ Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica​. The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Geometric Continuum Mechanics And Induced Beam Theories

Author: Simon Eugster
Publisher: Springer
ISBN: 3319164953
Size: 48.53 MB
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This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

David Hilbert And The Axiomatization Of Physics 1898 1918

Author: L. Corry
Publisher: Springer Science & Business Media
ISBN: 9781402027772
Size: 11.98 MB
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David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.

Fundamentals Of Structural Mechanics

Author: Keith D. Hjelmstad
Publisher: Springer Science & Business Media
ISBN: 0387233318
Size: 71.84 MB
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A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.

The Beauty Of Physics Patterns Principles And Perspectives

Author: A. R. P. Rau
Publisher: OUP Oxford
ISBN: 0191019895
Size: 17.19 MB
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The beauty of physics lies in its coherence in terms of a few fundamental concepts and principles. Even physicists have occasion to marvel at the overarching reach of basic principles and their ability to account for features stretching from the microscopic sub-atomic world to the cosmological expanses of the Universe. While mathematics is its natural language, physics is mostly about patterns, connections, and relations between objects and phenomena, and it is this aspect that is emphasized in this book. Since science tries to connect phenomena that at first sight appear widely different, while boiling them down to a small set of essential principles and laws, metaphor and analogy pervade our subject. Consider the pendulum, its swing from one extreme to the other often invoked in social or economic contexts. In molecular vibrations, such as in the CO2 molecule, the quantum motions of electrons and nuclei are metaphorically the pendulums. In electromagnetic radiation, including the visible light we observe, there are not even any concrete material particles, only electric and magnetic fields executing simple harmonic motion. But, to a physicist, they are all "just a pendulum". The selection of topics reflects the author's own four-decade career in research physics and his resultant perspective on the subject. While aimed primarily at physicists, including junior students, this book also addresses other readers who are willing to think with symbols and simple algebra in understanding the physical world around us. Each chapter, on themes such as dimensions, transformations, symmetries, or maps, begins with simple examples accessible to all while connecting them later to more sophisticated realizations in more advanced topics of physics.