拉格朗日及汉密尔敦力学：习题及解答LAGRANGIAN AND HAMILTONIAN MECHANICS

This book contains the exercises from the intermediate/advanced classical mechanics text Lagrangian and Hamiltonian Mechanics (World Scientific Pub. Co. Pte. Ltd., Singapore, 1996) together with their complete solutions. In a few of the exercises I have seen fit to make minor changes in the wording; these are marked by asterisks. Also, I have not included the f'mal Exercise 10-5, which is really an open-ended mini research project.
The present work is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course. It is hoped that it will assist them in choosing suitable assignments for their students, and that it will occasionally provide new insights. Instructors may also wish to photocopy and post the solutions to those exercises with which their students have had particular difficulty.
This book may also be used, together with Lagrangian and Hamiltonian Mechanics, by those who are studying mechanics on their own. In this case I strongly urge the individuals to make serious efforts to work out a substantial number of the
relevant exercises on completing their study of each chapter and before looking at what I have written here. Only in this way will such individuals come face to face with, and hopefully overcome, the various difficulties which the exercises present. Exercises, whether mental or physical, are meant to be done, not read about!

Preface
CHAPTER Ⅰ NEWTON'S LAWS
Exercise 1.01
Exercise 1.02
Exercise 1.03
Exercise 1.04
Exercise 1.05
Exercise 1.06
Exercise 1.07
Exercise 1.08
Exercise 1.09
Exercise 1.10
Exercise 1.11
Exercise 1.12
Exercise 1.13
Exercise 1.14
Exercise 1.15
Exercise 1.16
Exercise 1.17
Exercise 1.18
CHAPTER Ⅱ THE PRINCIPLE OF VIRTUAL WORK AND D'ALEMBERT' S PRINCIPLE
Exercise 2.01
Exercise 2.02
Exercise 2.03
Exercise 2.04
Exercise 2.05
Exercise 2.06
Exercise 2.07
Exercise 2.08
Exercise 2.09
Exericse 2.10
CHAPTER Ⅲ LAGRANGE'S EQUATIONS
Exercise 3.01
Exercise 3.02
Exercise 3.03
Exercise 3.04
Exercise 3.05
Exercise 3.06
Exercise 3.07
Exercise 3.08
Exercise 3.09
Exercise 3.10
Exercise 3.11
Exercise 3.12
Exercise 3.13
Exercise 3.14
Exercise 3.15
CHAPTER Ⅳ THE PRINCIPLE OF STATIONARY ACTION OR HAMILTON'S PRINCIPLE
Exercise 4.01
Exercise 4.02
Exercise 4.03
Exercise 4.04
Exercise 4.05
Exercise 4.06
Exercise 4.07
Exercise 4.08
Exercise 4.09
Exercise 4.10
Exercise 4.11
Exercise 4.12
CHAPTER Ⅴ INVARIANCE TRANSFORMATIONS AND CONSTANTS OF THE MOTION
CHAPTER Ⅵ HAMILTON'S EQUATIONS
CHAPTER Ⅶ CANONICAL TRANSFORMATIONS
CHAPTER Ⅷ HAMILTON-JACOBI THEORY
CHAPTER Ⅸ ACTION-ANGLE VARIABLES
CHAPTER Ⅹ NON-INTEGRABLE SYSTEMS