In this post, we will see the book Collection Of Problems In Classical Mechanics

by G. L. Kotkin; V. G. Serbo.

# About the book

This collection is meant for physics students. Its contents correspond roughly to the mechanics course in the textbooks by Landau and Lifshitz (I960), Goldstein (1950), or ter Haar (1964). We hope that the reading of this collection will give pleasure not only to students studying mechanics, but also to people who already know it. We follow the order in which the material is presented by Landau and Lifshitz, except that we start using the Lagrangian equations in § 4. The problems in §§ 1-3 can be solved using the Newtonian equations of motion together with the energy, linear momentum and angular momentum conservation laws. As a rule, the solution of a problem is not finished with obtaining the required formulae. It is necessary to analyse the results and this is of great interest and by no means a “mechanical” part of the solution. In particular, it is very desirable to study limiting cases. This is useful not only for checking purposes and for an understanding of the solution obtained, but also for a preliminary analysis of the problem which can be used to learn how to find the motion of a system by intuition. It is also very useful to investigate what happens to a solution, if the conditions of the problem are varied. We have, therefore, suggested further problems at the end of several solutions.

The book was translated from Russian by was published in by Publishers.

Credits to original uploader.

You can get the book here.

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# Contents

PREFACE

## PROBLEMS

1. Integration of One-dimensional Equations of Motion 3

2. Motion of a Particle in Three-dimensional Potentials 6

3. Scattering in a Given Field. Collisions between Particles 10

4. Lagrangian Equations of Motion. Conservation Laws 13

5. Small Oscillations of Systems with One Degree of Freedom 19

6. Small Oscillations of Systems with Several Degrees of Freedom 24

7. Oscillations of Linear Chains 34

8. Non-linear Oscillations 36

9. Rigid-body motion. Non-inertial Coordinate Systems 38

10. The Hamiltonian Equations of Motion 42

11. Poisson Brackets. Canonical Transformations 44

12. The Hamilton-Jacobi Equation 50

13. Adiabatic Invariants 53

## ANSWERS AND SOLUTIONS

1. Integration of One-dimensional Equations of Motion 63

2. Motion of a Particle in Three-dimensional Potentials 73

3. Scattering in a Given Field. Collisions between Particles 110

4. Lagrangian Equations of Motion. Conservation Laws 125

5. Small Oscillations of Systems with One Degree of Freedom 137

6. Small Oscillations of Systems with Several Degrees of Freedom 152

7. Oscillations of Linear Chains 183

8. Non-linear Oscillations 197

9. Rigid-body motion. Non-inertial Coordinate Systems 206

10. The Hamiltonian Equations of Motion 219

11. Poisson Brackets. Canonical Transformations 221

12. The Hamilton-Jacobi Equation 236

13. Adiabatic Invariants 253

REFERENCES 275

INDEX 277

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