Lagrangian Dynamics
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Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds
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Author : Taeyoung Lee
language : en
Publisher: Springer
Release Date : 2017-08-14
Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds written by Taeyoung Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.
This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
Lagrangian Fluid Dynamics
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Author : Andrew Bennett
language : en
Publisher: Cambridge University Press
Release Date : 2006-03-09
Lagrangian Fluid Dynamics written by Andrew Bennett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-09 with Mathematics categories.
This 2006 book provides a detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics.
Introduction To Lagrangian Mechanics An 2nd Edition
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Author : Alain J Brizard
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-11-28
Introduction To Lagrangian Mechanics An 2nd Edition written by Alain J Brizard and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Science categories.
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.
Introduction To Lagrangian Dynamics
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Author : Aron Wolf Pila
language : en
Publisher: Springer
Release Date : 2019-08-02
Introduction To Lagrangian Dynamics written by Aron Wolf Pila and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-02 with Technology & Engineering categories.
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
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Author : Alain Jean Brizard
language : en
Publisher: World Scientific
Release Date : 2008
An Introduction To Lagrangian Mechanics written by Alain Jean Brizard and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.This textbook is suitable for undergraduate students who have acquired the mathematical skills needed to complete a course in Modern Physics.
Lagrangian And Hamiltonian Dynamics
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Author : Peter Mann
language : en
Publisher: Oxford University Press
Release Date : 2018
Lagrangian And Hamiltonian Dynamics written by Peter Mann and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
Engineering Dynamics
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Author : Roger F. Gans
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-22
Engineering Dynamics written by Roger F. Gans and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-22 with Technology & Engineering categories.
This engineering dynamics textbook is aimed at beginning graduate students in mechanical engineering and other related engineering disciplines who need training in dynamics as applied to engineering mechanisms. It introduces the formal mathematical development of Lagrangian mechanics (and its corollaries), while solving numerous engineering applications. The author’s goal is to instill an understanding of the basic physics required for engineering dynamics, while providing a recipe (algorithm) for the simulation of engineering mechanisms such as robots. The book will be reasonably self-contained so that the practicing engineer interested in this area can also make use of it. This book is made accessible to the widest possible audience by numerous, solved examples and diagrams that apply the principles to real engineering applications. • Provides an applied textbook for intermediate/advanced engineering dynamics courses; • Discusses Lagrangian mechanics in the context of numerous engineering applications; • Includes numerous, solved examples, illustrative diagrams and applied exercises in every chapter
A Student S Guide To Lagrangians And Hamiltonians
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Author : Patrick Hamill
language : en
Publisher: Cambridge University Press
Release Date : 2014
A Student S Guide To Lagrangians And Hamiltonians written by Patrick Hamill and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Lagrangian And Hamiltonian Mechanics Solutions To The Exercises
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Author : Melvin G Calkin
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-03-12
Lagrangian And Hamiltonian Mechanics Solutions To The Exercises written by Melvin G Calkin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-12 with Science categories.
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.
Lagrangian Mechanics
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Author : Anh Le Van
language : en
Publisher: John Wiley & Sons
Release Date : 2019-06-18
Lagrangian Mechanics written by Anh Le Van and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-18 with Science categories.
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.