An elementary treatise on the dynamics of a particle and of rigid bodies / S.L Loney

Rs.7.00

PREFACE

In the following Rigid have tried to write an elementary class-book on those parts of Dynamics of a Particle and Rigid Dynamics which are usually read by Students attenarts of Dynamics lectures in Applied Mathematics for a Science or Engineering Degree, and by Junior Students for Mathematical Honours. Within the limits with which it professes to deal, I hope it will be found to be fairly complete.

I assume that the Student has previously read some such course as is included in my Elementary Dynamics. I also assume that he possesses a fair working knowledge of Differential and Integral Calculus; the Differential Equations, with which he will meet, are solved in the Text, and in an Appendix he will find a summary of the methods of solution of such equations

In Rigid Dynamics I have chiefly confined myself to two-dimensional motion, and I have omitted all reference to moving axes.

I have included in the book a large number of Examples, mostly collected from University and College Examination Papers; I have verified every question, and hope that there will not be found a large number of serious errors.

Solutions of the Examples have now been published. December, 1926

S.L. LONEY

PUBLISHER'S NOTE

This is a world wide acceptable book in Mathematics and Physics. The latest edition is also passed over a century. This book is retyped through LaTex and carefully read by the subject experts to make an error free edition. The overall format of the book remains unchanged. But the font size is improved specially the subscripts and superscipts which are sometimes difficult to visulize in the original edition or in the scaned versions. Little modifications are made for the cross references with respect to page numbers inside the text of the book which are changed due to the modified page and font sizes. An index has been added at the end of the book for easy searching a key-word by the reader. Figures are redrawn and placed properly in the text for clear understanding the theme.

Please note that the word 'shew' is used in the original edition of the book, it has been changed to 'show' in this edition. Since 'shew' is an archaic spelling of 'show'.

Professor Srimanta Pal, Indian Statistical Institute, carefully edited and reviewed this book, and also added answers of the given exercises as well as an index at the end of this book. This helps to the readers.

Suggestions from the reader are always wellcome for the improvement of the quality of the presentation of materials of the book.

July, 201

PUBLISHER

PART I

CONTENTS

DYNAMICS OF A PARTICLE

3-137

1. Fundamental Definitions And Principles..

3

9

2 Motion In A Straight Line....

3. Uniplanar Motion Where The Accelerations Parallelto Fixed Axes Are Given.

27

4. Uniplanar Motion Referred To Polar Coordinates Central Forces

5.

Uniplanar Motion When The Acceleration

37

Is Central And Varying As The Inverse Squareof The Distance

63

6. Tangential And Normal Accelerations: Uniplanar Constrained Motion

79

7. Motion In A Resisting Medium: Motion Of Particles Of Varying Mass

.97

8. Oscillatory Motion And Small Oscillations

111

9. Motion In Three Dimensions

125

10. Miscellaneous The Hodograph Motion On Revolving Curves. Impulsive Tensions Of Strings..

137

Part II

DYNAMICS OF RIGID BODYS

151-331

11. Moments And Products Of Inertia: Principal Axes..

151

12. D'alembert's Principle The General Equations Of Motion.

167

13. Motion About A Fixed Axis.

173

14. Motion In Two Dimensions. Finite Forces

193

15. Motion In Two Dimensions. Impulsive Forces

221

16. Instantaneous Centre: Angular Velocities Motion In Three Dimensions.

233

17. On The Principles Of The Conservation Of Momentum And Conservation Of Energy.

251

18. Lagrange's Equations In Generalised Coordinates....

271

19. Small Oscillations: Initial Motions

Tendency To Break.

285

20. Motion Of A Top

297

21. Miscellaneous Examples I

305

22. Miscellaneous Examples II

317

On The Solution Of Some Of The More Common

Forms Of Differential Equations

327

Index

331