# Lagrangian Mechanics

**Topics:**Lagrangian mechanics, Classical mechanics, Force

**Pages:**18 (5797 words)

**Published:**August 25, 2012

David J. Jeﬀery Physics Department New Mexico Tech Socorro, New Mexico

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Portpentagram Publishing (self-published) 2001 January 1

Introduction

Classical Mechanics Problems (CMP) is a source book for instructors of advanced classical mechanics at the Goldstein level. The book is available in electronic form to instructors by request to the author. It is free courseware and can be freely used and distributed, but not used for commercial purposes. The problems are grouped by topics in chapters: see Contents below. The chapter ordering follows the Goldstein chapter/topic ordering. For each chapter there are two classes of problems: in order of appearance in a chapter they are: (1) multiple-choice problems and (2) full-answer problems. Almost all the problems have complete suggested answers. The answers may be the greatest beneﬁt of CMP. The problems and answers can be posted on the web in pdf format. The problems have been suggested mainly by Goldstein problems, but have all been written by me. Given that the ideas for problems are the common coin of the realm, I prefer to call them redactions. Instructors, however, might well wish to ﬁnd solutions to particular problems from well known texts. Therefore, I give the suggesting source (when there is one or when I recall what it was) by a reference code on the extra keyword line: e.g., (Go3-29.1) stands for Goldstein (3rd Edition), p. 29, problem 1. Caveat: my redaction and the suggesting source problem will not in general correspond perfectly or even closely in some cases. The references for the source texts and other references follow the contents. A general citation is usually, e.g., Ar-400 for Arfken, p. 400. At the end of the book are two appendices. The ﬁrst is an equation sheet suitable to give to students as a test aid and a review sheet. The second is a set of answer tables for multiple choice questions. Classical Mechanics Problems is a book in progress. There are gaps in the coverage and the ordering of the problems by chapters is not yet ﬁnal. User instructors can, of course, add and modify as they list. Everything is written in plain TEX in my own idiosyncratic style. The questions are all have codes and keywords for easy selection electronically or by hand. A fortran program for selecting the problems and outputting them in quiz, assignment, and test formats is also available. Note the quiz, etc. creation procedure is a bit clonky, but it works. User instructors could easily construct their own programs for problem selection. I would like to thank the Physics Department of New Mexico Tech for its support for this work. Thanks also to the students who helped ﬂight-test the problems.

Contents

1 2 3 4 5 6 7 8 9 10 11 12 13 Elementary Problems and the Lagrangian Formulation Hamilton’s Principle and More on the Lagrangian Formulation The Central Force Problem Rigid Body Kinematics Rigid Body Equations of Motion Oscillations The Classical Mechanics of Special Relativity The Hamiltonian Formulation Canonical Transformations Hamilton-Jacobi Theory and Action-Angle Variables Classical Chaos Canonical Perturbation Theory Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields i

Appendices 1 Classical Mechanics Equation Sheet 2 Multiple-Choice Problem Answer Tables

References

Arfken, G. 1970, Mathematical Methods for Physicists (New York: Academic Press) (Ar) Bevington, P. R. 1969, Data Reduction and Error Analysis for the Physical Sciences (New-York: McGraw-Hill Book Company) (Be) Enge, H. A. 1966, Introduction to Nuclear Physics (Reading, Massachusetts: Addison-Wesley Publishing Company, Inc.) (En) Goldstein, H. 1980, Classical Mechanics, 2nd Edition (Reading, Massachusetts: Addison-Wesley Publishing Company) (Go2) Goldstein, H., Poole, C. P., Jr., & Safko, J. L. 2002, Classical Mechanics, 3rd Edition (San Francisco: Addison-Wesley Publishing Company) (Go3)

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