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A Primer Of Analytical Mechanics
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Book Synopsis A Primer of Analytical Mechanics by : Franco Strocchi
Download or read book A Primer of Analytical Mechanics written by Franco Strocchi and published by Springer. This book was released on 2018-03-09 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a “gauge” transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.
Book Synopsis A Primer of Analytical Mechanics by : F. Strocchi
Download or read book A Primer of Analytical Mechanics written by F. Strocchi and published by . This book was released on 2018 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a "gauge" transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book's closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.
Book Synopsis Analytical Mechanics by : Carl S. Helrich
Download or read book Analytical Mechanics written by Carl S. Helrich and published by Springer. This book was released on 2016-10-01 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.
Book Synopsis Analytical Mechanics by : A.I. Lurie
Download or read book Analytical Mechanics written by A.I. Lurie and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 859 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a translation of A.I. Lurie’s classical Russian textbook on analytical mechanics. It offers a consummate exposition of the subject of analytical mechanics through a deep analysis of its most fundamental concepts. The book has served as a desk text for at least two generations of researchers working in those fields where the Soviet Union accomplished the greatest technological breakthrough of the 20th century - a race into space. Those and other related fields continue to be intensively explored since then, and the book clearly demonstrates how the fundamental concepts of mechanics work in the context of up-to-date engineering problems.
Book Synopsis Analytical Mechanics by : Nivaldo A. Lemos
Download or read book Analytical Mechanics written by Nivaldo A. Lemos and published by Cambridge University Press. This book was released on 2018-08-09 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analytical mechanics.
Book Synopsis A Treatise Upon Analytical Mechanics by : Pierre Simon marquis de Laplace
Download or read book A Treatise Upon Analytical Mechanics written by Pierre Simon marquis de Laplace and published by . This book was released on 1814 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytical Mechanics by : Antonio Fasano
Download or read book Analytical Mechanics written by Antonio Fasano and published by OUP Oxford. This book was released on 2006-04-06 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics, with remarkable applications to many branches of physics (Astronomy, Statistical and Quantum Mechanics, etc.). Rooted in the works of Lagrange, Euler, and Poincaré, it is a classical subject with fascinating developments and still rich with open problems. It addresses such fundamental questions as: Is the solar system stable? Is there a unifying "economy" principle in mechanics? How can a point mass be described as a "wave"? This book was written to fill a gap between elementary expositions and more advanced (and clearly more stimulating) material. It takes the challenge to explain the most relevant ideas and to show the most important applications using plain language and "simple" mathematics, often through an original approach. Basic calculus is enough for the reader to proceed through the book and when more is required, the new mathematical concepts are illustrated, again in plain language. The book is conceived in such a way that some difficult chapters can be bypassed, whilst still grasping the main ideas. However, anybody wishing to go deeper in some directions will find at least the flavour of recent developments and many bibliographical references. Theory is always accompanied by examples. Many problems are suggested and some are completely worked out at the end of each chapter. The book may effectively be used (and it is in several Italian Universities) for undergraduate as well as for PhD courses in Physics and Mathematics at various levels.
Book Synopsis Analytical Mechanics by : J.L. Lagrange
Download or read book Analytical Mechanics written by J.L. Lagrange and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mécanique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.
Book Synopsis Analytical Mechanics by : Joseph S. Torok
Download or read book Analytical Mechanics written by Joseph S. Torok and published by John Wiley & Sons. This book was released on 1999-11-04 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literatur zur analytischen Mechanik enthalt meist nur die klassische Theorie, an der sich seit Jahren nichts geandert hat. Dieses Buch fullt eine Lucke, indem es rund 250 neue Beispiele und rund 400 neue Aufgaben bietet sowie nun auch computergestutzte Rechenmethoden behandelt. Mathematische Theorie und ingenieurtechnische Anwendungen stehen dabei stets in einem ausgewogenen Verhaltnis zueinander. Mit vielen anschaulichen Abbildungen! (11/99)
Book Synopsis A Student's Guide to Analytical Mechanics by : John L. Bohn
Download or read book A Student's Guide to Analytical Mechanics written by John L. Bohn and published by Cambridge University Press. This book was released on 2018-08-30 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible guide to analytical mechanics, using intuitive examples to illustrate the underlying mathematics, helping students formulate, solve and interpret problems in mechanics.
Book Synopsis Introduction to Analytical Mechanics by : Alexander Ziwet
Download or read book Introduction to Analytical Mechanics written by Alexander Ziwet and published by . This book was released on 1912 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Student's Guide to Analytical Mechanics by : John L. Bohn
Download or read book A Student's Guide to Analytical Mechanics written by John L. Bohn and published by Cambridge University Press. This book was released on 2018-08-30 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical mechanics is a set of mathematical tools used to describe a wide range of physical systems, both in classical mechanics and beyond. It offers a powerful and elegant alternative to Newtonian mechanics; however it can be challenging to learn due to its high degree of mathematical complexity. Designed to offer a more intuitive guide to this abstract topic, this guide explains the mathematical theory underlying analytical mechanics; helping students to formulate, solve and interpret complex problems using these analytical tools. Each chapter begins with an example of a physical system to illustrate the theoretical steps to be developed in that chapter, and ends with a set of exercises to further develop students' understanding. The book presents the fundamentals of the subject in depth before extending the theory to more elaborate systems, and includes a further reading section to ensure that this is an accessible companion to all standard textbooks.
Author :K. A. I. L. W. Gamalath Publisher :Alpha Science International, Limited ISBN 13 :9781842656686 Total Pages :0 pages Book Rating :4.6/5 (566 download)
Book Synopsis Introduction to Analytical Mechanics by : K. A. I. L. W. Gamalath
Download or read book Introduction to Analytical Mechanics written by K. A. I. L. W. Gamalath and published by Alpha Science International, Limited. This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a modern treatment of classical mechanics so that transition to many fields in physics can be made with the least difficulty. This book deals with the formulation of Newtonian mechanics, Lagrangian dynamics, which are formulating the quantum mechanics and Hamilton-Jacobi equation which provides the transition to wave mechanics.
Book Synopsis Analytical Mechanics for Engineers by : Fred B. Seely
Download or read book Analytical Mechanics for Engineers written by Fred B. Seely and published by . This book was released on 1927 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytical Mechanics by : Ioan Merches
Download or read book Analytical Mechanics written by Ioan Merches and published by CRC Press. This book was released on 2014-08-26 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive a
Book Synopsis Lagrangian Mechanics by : Anh Le Van
Download or read book Lagrangian Mechanics written by Anh Le Van and published by John Wiley & Sons. This book was released on 2019-06-03 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lagrangian Mechanics explains the subtleties of analytical mechanics and its applications in rigid body mechanics. The authors demonstrate the primordial role of parameterization, which conditions the equations and thus the information obtained; the essential notions of virtual kinematics, such as the virtual derivative and the dependence of the virtual quantities with respect to a reference frame; and the key concept of perfect joints and their intrinsic character, namely the invariance of the fields of compatible virtual velocities with respect to the parameterization. Throughout the book, any demonstrated results are stated with the respective hypotheses, clearly indicating the applicability conditions for the results to be ready for use. Numerous examples accompany the text, facilitating the understanding of the calculation mechanisms. The book is mainly intended for Bachelor's, Master's or engineering students who are interested in an in-depth study of analytical mechanics and its applications.
Book Synopsis Analytical Mechanics by : Grant Robert FOWLES
Download or read book Analytical Mechanics written by Grant Robert FOWLES and published by . This book was released on 1962 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
