Introduction To Lagrangian Mechanics, An (2nd Edition)

Introduction To Lagrangian Mechanics, An (2nd Edition)
Author: Alain J Brizard
Publisher: World Scientific Publishing Company
Total Pages: 324
Release: 2014-11-28
Genre: Science
ISBN: 9814623644

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.

A Student's Guide to Lagrangians and Hamiltonians

A Student's Guide to Lagrangians and Hamiltonians
Author: Patrick Hamill
Publisher: Cambridge University Press
Total Pages: 185
Release: 2014
Genre: Mathematics
ISBN: 1107042887

A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds
Author: Taeyoung Lee
Publisher: Springer
Total Pages: 561
Release: 2017-08-14
Genre: Mathematics
ISBN: 3319569538

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.

Introduction to Analytical Dynamics

Introduction to Analytical Dynamics
Author: Nicholas Woodhouse
Publisher: Springer Science & Business Media
Total Pages: 240
Release: 2009-12-17
Genre: Science
ISBN: 1848828160

First published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding.

Modern Robotics

Modern Robotics
Author: Kevin M. Lynch
Publisher: Cambridge University Press
Total Pages: 545
Release: 2017-05-25
Genre: Computers
ISBN: 1107156300

A modern and unified treatment of the mechanics, planning, and control of robots, suitable for a first course in robotics.

Lagrangian Fluid Dynamics

Lagrangian Fluid Dynamics
Author: Andrew Bennett
Publisher: Cambridge University Press
Total Pages: 23
Release: 2006-03-09
Genre: Mathematics
ISBN: 0521853109

This 2006 book provides a detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics.

No-Nonsense Classical Mechanics

No-Nonsense Classical Mechanics
Author: Jakob Schwichtenberg
Publisher: No-Nonsense Books
Total Pages: 393
Release: 2019-04-30
Genre: Science
ISBN:

Learning classical mechanics doesn’t have to be hard What if there was a way to learn classical mechanics without all the usual fluff? What if there were a book that allowed you to see the whole picture and not just tiny parts of it? Thoughts like this are the reason that No-Nonsense Classical Mechanics now exists. What will you learn from this book? Get to know all fundamental mechanics concepts — Grasp why we can describe classical mechanics using the Lagrangian formalism, the Newtonian formalism, or the Hamiltonian formalism and how these frameworks are connected.Learn to describe classical mechanics mathematically — Understand the meaning and origin of the most important equations: Newton's second law, the Euler-Lagrange equation and Hamilton's equations.Master the most important classical mechanics systems — Read fully annotated, step-by-step calculations and understand the general algorithm we use to describe them.Get an understanding you can be proud of — Learn about beautiful and deep insights like Noether's theorem or Liouville's theorem and how classical mechanics emerges in a proper limit of special relativity, quantum mechanics and general relativity. No-Nonsense Classical Mechanics is the most student-friendly book on classical nechanics ever written. Here’s why. First of all, it's is nothing like a formal university lecture. Instead, it’s like a casual conservation with a more experienced student. This also means that nothing is assumed to be “obvious” or “easy to see”.Each chapter, each section, and each page focuses solely on the goal to help you understand. Nothing is introduced without a thorough motivation and it is always clear where each equation comes from.The book contains no fluff since unnecessary content quickly leads to confusion. Instead, it ruthlessly focuses on the fundamentals and makes sure you’ll understand them in detail. The primary focus on the readers’ needs is also visible in dozens of small features that you won’t find in any other textbook In total, the book contains more than 100 illustrations that help you understand the most important concepts visually. In each chapter, you’ll find fully annotated equations and calculations are done carefully step-by-step. This makes it much easier to understand what’s going on in.Whenever a concept is used that was already introduced previously there is a short sidenote that reminds you where it was first introduced and often recites the main points. In addition, there are summaries at the beginning of each chapter that make sure you won’t get lost.

Lagrangian And Hamiltonian Mechanics: Solutions To The Exercises

Lagrangian And Hamiltonian Mechanics: Solutions To The Exercises
Author: Melvin G Calkin
Publisher: World Scientific Publishing Company
Total Pages: 240
Release: 1999-03-12
Genre: Science
ISBN: 9813105410

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 and Hamiltonian Dynamics

Lagrangian and Hamiltonian Dynamics
Author: Peter Mann
Publisher: Oxford University Press
Total Pages: 553
Release: 2018
Genre: Mathematics
ISBN: 0198822375

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.

Introduction to Dynamics

Introduction to Dynamics
Author: Ian Percival
Publisher: Cambridge University Press
Total Pages: 242
Release: 1982-12-02
Genre: Mathematics
ISBN: 9780521281492

In this book, the subject of dynamics is introduced at undergraduate level through the elementary qualitative theory of differential equations, the geometry of phase curves and the theory of stability. The text is supplemented with over a hundred exercises.