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This book is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.

This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.

This book is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.

This book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussion of topics such as invariance, Hamiltonian Jacobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical "hidden"; momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the "(e/c)A"; term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton Jacobi equation of mechanics, the eikonal equation of optics, and the Schrödinger equation of quantum mechanics. The text contains 115 exercises. This text is suitable for a course in classical mechanics at the advanced undergraduate level.

This book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussion of topics such as invariance, Hamiltonian Jacobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical "hidden"; momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the "(e/c)A"; term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton Jacobi equation of mechanics, the eikonal equation of optics, and the Schrödinger equation of quantum mechanics. The text contains 115 exercises. This text is suitable for a course in classical mechanics at the advanced undergraduate level.

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers.Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications.The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers.Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications.The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.

This volume provides a short summary of the essentials of Lagrangian dynamics for practicing engineers and students of physics and engineering. It examines a range of phenomena and techniques in a style that is compact and succinct, while remaining comprehensive. The book provides a review of classical mechanics and coverage of critical topics including holonomic and non-holonomic systems, virtual work, the principle of d’Alembert for dynamical systems, the mathematics of conservative forces, the extended Hamilton’s principle, Lagrange’s equations and Lagrangian dynamics, a systematic procedure for generalized forces, quasi-coordinates, and quasi-velocities, Lagrangian dynamics with quasi-coordinates, Professor Ranjan Vepa’s approach and the Hamiltonian formulation. Adopting a step-by-step approach with examples throughout the book, this ready reference completely develops all of the relevant equations and is ideal for practicing mechanical, aeronautical, and civil engineers, physicists, and graduate/upper-level undergraduate students.Explains in detail the development of the theory behind Lagrangian dynamics in a practical fashion;Discusses virtual work, generalized forces, conservative forces, constraints, Extended Hamilton’s Principle and the Hamiltonian formulation;Presents two different approaches to the quasi-velocity method for non-holonomic constraints;Reinforces concepts presented with illustrative examples;Includes comprehensive coverage of the important topics of classical mechanics.

 An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler–Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics.New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.

The book clearly and concisely explains the basic principles of Lagrangian dynamicsand provides training in the actual physical and mathematical techniques of applying Lagrange's equations, laying the foundation for a later study of topics that bridge the gap between classical and quantum physics, engineering, chemistry and applied mathematics, and for practicing scientists and engineers.

A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler-Lagrange equations. It introduces Hamilton's principle and uses this throughout the book to derive further results. The Hamiltonian, Hamilton's equations, canonical transformations, Poisson brackets and Hamilton-Jacobi theory are considered next. The book concludes by discussing continuous Lagrangians and Hamiltonians and how they are related to field theory. Written in clear, simple language and featuring numerous worked examples and exercises to help students master the material, this book is a valuable supplement to courses in mechanics.

The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.

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A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler-Lagrange equations. It introduces Hamilton's principle and uses this throughout the book to derive further results. The Hamiltonian, Hamilton's equations, canonical transformations, Poisson brackets and Hamilton-Jacobi theory are considered next. The book concludes by discussing continuous Lagrangians and Hamiltonians and how they are related to field theory. Written in clear, simple language and featuring numerous worked examples and exercises to help students master the material, this book is a valuable supplement to courses in mechanics.

Ancien livre de bibliothèque. Traces d'usure sur la couverture. Couverture différente. Edition 1975. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Good. Former library book. Signs of wear on the cover. Different cover. Edition 1975. Ammareal gives back up to 15% of this item's net price to charity organizations.

This book is an introduction to level set methods, which are powerful numerical techniques for analysing and computing interface motion in a host of settings. They rely on a fundamental shift in how one views moving boundaries; rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. The resulting numerical techniques can be used to track three-dimensional complex fronts that can develop sharp corners and change topology as they evolve. A large collection of applications is provided in the text, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision and control theory. This book will be a useful resource for mathematicians, applied scientists, practising engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

Robot Modeling and Control introduces the fundamentals of robot modeling and control and provides background material on terminology, linear algebra, dynamical systems and stability theory, followed by detailed coverage of forward and in-verse kinematics, Jacobians, Lagrangian dynamics, motion planning, robust and adaptive motion and force control, and com-puter vision.  Both basic and advanced material is presented in a style that is readable and mathematically rigorous.  The book provides relevant applications from industrial robotics and mobile robotics. Suitable for a one or two term course, this text is appropriate for undergraduate and graduate students from electrical engineering, mechanical engineering, computer science, and mathematics and can be used as a research reference. Many detailed worked examples and extensive problems illustrate theory and point the reader to more advanced topics.