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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 treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
simulated motion on a computer screen, and to study the effects of changing parameters. --
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.
Study faster, learn better--and get top grades with Schaum's Outlines Millions of students trust Schaum's Outlines to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. Use Schaum's Outlines to: Brush up before tests Find answers fast Study quickly and more effectively Get the big picture without spending hours poring over lengthy textbooks Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores! This Schaum's Outline gives you: A concise guide to the standard college course influid dynamics 480 problems with answers or worked-out solutions Practice problems in multiple-choice format like thoseon the Fundamentals of Engineering Exam
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.
Publisher description -- This book will save you time as you master the basics taught in first-year, calculus-based college physics courses. You'll firmly grasp the all-important building blocks needed for every physical science and all branches of engineering. The many problems included with guided solutions make this potentially daunting subject much easier. Additional problems with answers give you a chance to reinforce what you've learned and gauge your progress as you go. This next-best thing to a private tutor makes especially clear the topics most students find most difficult. It's ideal for independent study, brushup before an exam, or preparation for the MED-CAT and GRE.
Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.
A practical approach to the computational methods used to solve real-world dynamics problems Computational dynamics has grown rapidly in recent years with the advent of high-speed digital computers and the need to develop simulation and analysis computational capabilities for mechanical and aerospace systems that consist of interconnected bodies. Computational Dynamics, Second Edition offers a full introduction to the concepts, definitions, and techniques used in multibody dynamics and presents essential topics concerning kinematics and dynamics of motion in two and three dimensions. Skillfully organized into eight chapters that mirror the standard learning sequence of computational dynamics courses, this Second Edition begins with a discussion of classical techniques that review some of the fundamental concepts and formulations in the general field of dynamics. Next, it builds on these concepts in order to demonstrate the use of the methods as the foundation for the study of computational dynamics. Finally, the book presents different computational methodologies used in the computer-aided analysis of mechanical and aerospace systems. Each chapter features simple examples that show the main ideas and procedures, as well as straightforward problem sets that facilitate learning and help readers build problem-solving skills. Clearly written and ready to apply, Computational Dynamics, Second Edition is a valuable reference for both aspiring and practicing mechanical and aerospace engineers.