## Theoretical Mechanics – A Short Course -Targ

In this post, we will see the book Theoretical Mechanics – A Short Course by S. Targ.

This Short Course of Theoretical Mechanics is designed for students of higher and secondary technical schools. It treats of the basic methods of theoretical mechanics and spheres of their application along with some to­pics which are of such importance todays that no course of mechanics, even a short one, can neglect them altogether.

In preparing the original Russian edition for translation the text has be­en substantially revised, with additions, changes and corrections in practi­cally all the chapters.

Most of the additions are new sections containing supplementary infor­mation on the motion of a rigid body about a fixed point (the kinematic and dynamic Euler equations) and chapters setting forth the fundamentals of the method of generalized coordinates (the Lagrange equations), since the de­mands to the course of theoretical mechanics in training engineers of diffe­rent specialities makes it necessary to devote some space to this subject even in a short course.

Also the book presents an essential minimum on the elementary theory of the gyroscope and such highly relevant topics as motion in gravitational fields (elliptical paths and space flights) and the motion of a body of va­riable mass (rocket motion); a new section discusses weightlessness.

The structure of this book is based on the profound conviction, born out by many years of experience, that the best way of presenting study mate­rial, especially when it is contained in a short course, is to proceed from the particular to the general. Accordingly, in this book, plane statics comes be­fore three-dimensional statics, particle dynamics before system dynamics, rectilinear motion before curvilinear motion, etc. Such an arrangement helps the student to understand and digest the material better and faster and the teaching process itself is made more graphic and consistent.

Alongside with the geometrical and analytical methods of mechanics the book makes wide use of the vector method as one of the main generally accepted methods, which, furthermore, possesses a number of indisputable advantages. As a rule, however, only those vector operations are used which are similar to corresponding operations with scalar quantities and which do not require an acquaintance with many new concepts.

Considerable space—more than one-third of the book—is devoted to examples and worked problems. They were chosen with an eve to ensure a clear comprehension of the relevant mechanical phenomena and cover all the main types of problems solved by the methods described. There are 176 such examples (besides worked problems); their solutions contain instruc­tions designed to assist the student in his independent work on the course. In this respect the book should prove useful to all students of engineering, notably those studying by correspondence or on their own.

The book was translated from the Russian by V. Talmy.

There are several editions and reprints of the book. First, it was published under Foreign Languages Publishing House in the 1950s and 1960s, later under Mir, with the last reprint in 1988.

This post has copies from both Mir (Link 1) and FLPH (Links 2 and 3).

Link 1 (Mir 1988 reprint, credits to the original uploader, converted djvu to pdf [I am not a big fan of djvu format], added pagination, bookmarks, OCR and cover)

Link 2 (FLPH 1960s print, cleaned, bookmarked, paginated copy of the link below. Note that this is not a hi-resolution scan, though the OCR has worked well for most of the words. A better copy could be suggested.)

Link 3 (from Public Resource collection, original for the cleaned copy above)

## CONTENTS

Note: The contents of the FLPH and Mir editions are a bit different. There is slight reorganisation of the topics and a few new topics in the Mir edition and it has 32 chapters, one more than the FLPH edition and more pages 528 as compared to 427 in FLPH edition.

## Contents (Mir 1988 edition)

Preface to the English Edition 5

Introduction 15

Part 1. STATICS OF RIGID BODIES

Chapter 1. Basic Concepts and Principles

1. The subject of statics 19
2. Force 21
3. Fundamental principles 22
4. Constraints and their reactions 26
5. Axiom of constraints 28

Chapter 2. Composition of Forces. Concurrent Force Systems

6. Geometrical method of composition of forces. Resultant of con­ current forces 30
7. Resolution of forces 32
8. Projection of a force on an axis and on a plane 36
9. Analytical method of defining a force 37
10. Analytical method of composition of forces 38
11. Equilibrium of a system of concurrent forces 40
12. Problems statically determinate and statically indeterminate 42
13. Solution of problems of statics 43
14. Moment of force about an axis (or a point) 53
15. Varignon’s theorem of the moment of a resultant 54
16*. Equations of moments of concurrent forces 55

Chapter 3. Parallel Forces and Force Couples in a Plane 64

17. Composition and resolution of parallel forces 58
18. A force couple. Moment of a couple 60
19. Equivalent couples 62
20. Composition of coplanar couples. Conditions for the equilibrium of couples 64

Chapter 4. General Case of Forces in a Plane

21. Theorem of translation of a force 67
22. Reduction of a coplanar force system to a givencentre 68
23. Reduction of a coplanar force system to the simplestpossible form 71
24. Conditions for the equilibrium of a coplanar force system. The case of parallel forces 73
25. Solution of problems 75
26. Equilibrium of systems of bodies 84
27*. Determination of internal forces (stresses) 88
28*. Distributed forces 89

Chapter 5. Elements of Graphical Statics

29. Force and string polygons. Reduction of a coplanar force system to two forces 93
30. Graphical determination of a resultant 95
31. Graphical determination of a resultant couple 96
32. Graphical conditions of equilibrium of a coplanarforce system 96
33. Determination of the reactions of constraints 97

Chapter 6. Solution of Trusses

34. Trusses. Analytical analysis of plane trusses 99
35*. Graphical analysis of plane trusses 103
36*. The Maxwell-Cremona diagram 104

Chapter 7. Friction

37. Laws of static friction 107
38. Reactions of rough constraints. Angle offriction 109
39. Equilibrium with friction 110
40*. Belt friction 114
41*. Rolling friction and pivot friction 116

Chapter 8. Couples and Forces in Space

42. Moment of a force about a point as a vector 118
43. Moment of a force with respect to an axis 120
44. Relation between the moments of a force about a point and an axis 123
45. Vector expression of the moment of a couple 124
46*. Composition of couples in space. Conditions of equilibrium of couples 125
47. Reduction of a force system in space to a given centre 128
48*. Reduction of a force system in space to the simplest possible form 130
49. Conditions of equilibrium of an arbitrary force system in space.
The case of^ parallel forces 132
50. Varignon’s theorem of the moment of a resultant with respect to
an axis 134
51. Problems on equilibrium of bodies subjected to action of force systems in space 134
52*. Conditions of equilibrium of a constrained rigid body. Concept of stability of equilibrium 144

Chapter 9. Centre of Gravity

53. Centre of parallel forces 146
54. Centre of gravity of a rigid body 148
55. Coordinates of centres of gravity of homogeneous bodies 149
56. Methods of determining the coordinates of the centre of gravity of bodies 150
57. Centres of gravity of some homogeneous bodies 153

Part 2 KINEMATICS OF A PARTICLE AND A RIGID BODY

Chapter 10. Kinematics of a Particle

58. Introduction to kinematics 156
59. Methods of describing motion of a particle. Path 158
60*. Conversion from coordinate to natural method of describing its motion is described by the coordinate method 161
61. Velocity vector of a particle 163
62. Acceleration vector of a particle 164
63. Theorem of the projection of the derivativeof a vector 166
64. Determination of the velocity and acceleration of a particle when its motion is described by coordinate method 167
65. Solution of problems of particle kinematics 168
66. Determination of the velocity of a particle when its motion is described by the natural method 173
67. Tangential and normal accelerations of a particle 174
68. Some special cases of particle motion 178
69. Graphs of displacement, velocity and acceleration of a particle 180
70. Solution of problems 182
71*. Velocity in polar coordinates 185
72*. Graphical analysis of particle motion 186

Chapter 11. Translational and Rotational Motion of a Rigid Body

73. Translational motion 191
74. Rotational motion of a rigid body. Angular velocity and angular acceleration 193
75. Uniform and uniformly variable rotations 195
76. Velocities and accelerations of the points of a rotating body 196

Chapter 12. Plane Motion of a Rigid Body

77. Equations of plane motion. Resolution of motion into translation and rotation 201
78. Determination of the path of a point of a body 203
79. Determination of the velocity of a point of a body 204
80. Theorem of the projections of the velocities of two points of a body 206
81. Determination of the velocity of a point of a body using the in­stantaneous centre of zero velocity. Centrodes 207
82. Solution of problems 212
83*. Velocity diagram 217
84. Determination of the acceleration of a point of a body 219
85*. Instantaneous centre of zero acceleration 227

Chapter 13. Motion of a Rigid Body Having One Fixed Point and Motion of a Free Rigid Body

86. Motion of a rigid body having one fixed point 231
87*. Velocity and acceleration of a point of a body 233
88. The general motion of a free rigid body 236

Chapter 14. Resultant Motion of a Particle

89. Relative, transport, and absolute motion 239
90. Composition of velocities 241
91*. Composition of accelerations 245
92. Solution of problems 249

Chapter 15. Resultant Motion of a Rigid Body

93. Composition of translational motions 257
94. Composition of rotations about two parallel axes 257
95*. Toothed spur gearing 260
96*. Composition of rotations about intersecting axes 264
97*. Euler kinematic equations 266
98*. Composition of a translation and a rotation. Screwmotion 268

Part 3 PARTICLE DYNAMICS

Chapter 16. Introduction of Dynamics. Laws of Dynamics

99. Basic concepts and definitions 271
100. The laws of dynamics 273
101. Systems of units 275
102. The problems of dynamics for a free and a constrained particle 275
103. Solution of the first problem of dynamics (determination of the forces if the motion is known) 276

Chapter 17. Differential Equations of Motion for a Particle and Their Integration

104. Rectilinear motion of a particle 279
105. Solution of problems 282
106*. Body falling in a resisting medium (in air) 288
107. Curvilinear motion of a particle 291
108. Motion of a particle thrown at an angle to the horizon in a uniform gravitational field 292

Chapter 18. General Theorems of Particle Dynamics

109. Momentum and kinetic energy of a particle 295
110. Impulse of a force 296
111. Theorem of the change in the momentum of a particle 297
112. Work done by a force. Power 298
113. Examples of calculation of work 302
114. Theorem of the change in the kinetic energy of a particle 306
115. Solution of problems 307
116. Theorem of the change in the angular momentum of a particle
(the principle of moments) 315
117*. Motion under the action of a central force. Law of areas 317

Chapter 19. Constrained Motion of a Particle

§ 118. Equations of motion of a particle along a given fixed curve 319 § 119. Determination of the reactions of constraints 322

Chapter 20. Relative Motion of a Particle

120. Equations of relative motion and rest of a particle 325
121. Effect of the rotation of the earth on the equilibrium and motion of bodies 328
122*.Deflection of a falling particle from the vertical by the earth’s rotation 331

Chapter 21. Rectilinear Vibration of a Particle

123. Free vibrations neglecting resisting forces 335
124. Free vibration with a resisting force proportional to velocity (damped vibration) 341
125. Forced vibration. Resonance 343

Chapter 22*. Motion of a Body in the Earth’s Gravitational Field

126. Motion of a particle thrown at an angle to the horizon in the earth’s gravitational field 353
127. Artificial earth satellites. Elliptical paths 357
128. Weightlessness 360

Part 4 DYNAMICS OF A SYSTEM AND A RIGID BODY

Chapter 23. Introduction to the Dynamics of a System. Moments of Inertia of Rigid Bodies

129. Mechanical systems. External and internal forces 366
130. Mass of a system. Centre of mass 367
131. Moment of inertia of a body about an axis. Radius of gyration 368
132. Moments of inertia of a body about parallel axes. The parallel axis (Huygens’) theorem 372
133*. Product of inertia. Principal axes of inertia of a body 374

Chapter 24. Theorem of the Motion of the Centre of Mass of a System

134. The differential equations of motion of a system 378
135. Theorem of motion of centre of mass 379
136. The law of conservation of motion of centre of mass 380
137. Solution of problems 382

Chapter 25. Theorem of the Change in the Linear Momentum of a System

138. Linear momentum of a system 387
139. Theorem of the change in linear momentum 388
140. The law of conservation of linear momentum 389
141. Solution of problems 391
142*. Bodies having variable mass. Motion of a rocket 393

Chapter 26. Theorem of the Change in the Angular Momentum of a System

143. Total angular momentum of a system 397
144. Theorem of the change in the total angular momentum of a system (the principle of moments) 399
145. The law of conservation of the total angular momentum 401
146. Solution of problems 403

Chapter 27. Theorem of the Change in the Kinetic Energy of a System

147. Kinetic energy of a system 407
148. Some cases of computation of work 411
149. Theorem of the change in the kinetic energy of a system 414
150. Solution of problems 416
151. Conservative force field and force function 422
152. Potential energy 426
153. The law of conservation of mechanical energy 427

Chapter 28. Applications of the General Theorems to Rigid-body Dynamics

154. Rotation of a rigid body 429
155. The compound pendulum 432
156. Plane motion of a rigid body 435
157*. Approximate theory of gyroscopic action 443
158*. Motion of a rigid body about a fixed point and motion of a free rigid body 448

Chapter 29. Applications of the General Theorems to the Theory of Impact

159. The fundamental equation of the theory of impact 454
160. General theorems of the theory of impact 455
161. Coefficient of restitution 457
162. Impact of a body against a fixed obstacle 458
163. Direct central impact of two bodies (impact of spheres) 460
164. Loss of kinetic energy in perfectly inelastic impact. Carnot’s theorem 462 165*. Impact with a rotating body 464

Chapter 30. D’Alembert’s Principle. Forces Acting on the Axis of a Rotating Body

166. D’Alembert’s principle 469
167. The principal vector and the principal moment of the inertia forces of a rigid body 472
168. Solution of problems 473
169*. Dynamic reactions on the axis of a rotating body. Dynamic balancing of masses 479

Chapter 31. The Principle of Virtual Displacements and the General Equation of Dynamics 485

170. Virtual displacements of a system. Degrees of freedom 485
171. The principle of virtual displacements 486
172. Solution of problems 488
173. The general equation of dynamics 494

Chapter 32*. Equilibrium Conditions and Equations of Motion of a System in Generalised Coordinates 499

174. Generalised coordinates and generalised velocities 499
175. Generalised forces 501
176. Equilibrium conditions for a system in generalised coordinates 505
177. Lagrange’s equations 507
178. Solution of problems 510

Index 520

## Contents (FLPH 1960s edition)

Preface 9

Introduction 10

PART 1. STATICS OF RIGID BODIES

Chapter 1. Basic Concepts and Principles

1. The Subject of Statics 13
2. Force 14
3. Fundamental Principles 16
4. Constraints and Their Reactions 19
5. Axiom of Constraints 22

Chapter 2. Concurrent Force Systems

6. Geometrical method of Composition of forces. Concurrent Forces 23
7. Resolution of Forces 25
8. Projection of a Force on an Axis and on a Plane 28
9. Analytical Method ol Defining a Force 30
10. Analytical Method for (he Composition of Forces 31
11. Equilibrium of a System of Concurrent Forces 32
12. Problems Statically Determinate and Statically Indeterminate 34
13. Solution of Problems of Statics 35
14. Moment of a Force About an Axis (or a Point) 43
15. Varignon’s Theorem of the moment of a Resultant 45
16. Equations of Moments of Concurrent Forces 46

Chapter 3. Parallel Forces and Couples in a Plane

17. Composition and Resolution of Parallel Forces 47
18. Force Couples. Moment of a Couple 50
19. Equivalent Couples 51
20. Coplanar Couples. Conditions for the Equilibrium of couples 53

Chapter 4. General Case of Forces in a Plane

21. Theorem of the Translation of a Force to a Parallel Position 55
22. Reduction of a Coplanar Force System to a Given Centre 56
23. Reduction of a Coplanar Force System to the Simplest Possible Form 58
24. Conditions for the Equilibrium of a Coplanar Force System 61
25. Equilibrium of a Coplanar System of Parallel Forces 63
26. Solution of Problems 63
27. Equilibrium of Systems of Bodies 70
28. Distributed Forces 74

Chapter 5. Elements of Graphical Statics

29. Force and String Polygons. Reduction of a Coplanar Force Systems to Two Forces 78
30. Graphical Determination of a Resultant 80
31. Graphical Determination of a Resultant Couple 80
32. Graphical Conditions of Equilibrium of a Coplanar Force System 81
33. Determination of the Reactions of Constraints 81
34. Graphical Analysis of Plane Trusses 82
35. The Maxwell Diagram 85

Chapter 6. Friclion

36. Laws of Static Friction 86
37. Reactions of Rough Constraints. Angle of Friction 88
38. Equilibrium with Friction 89
39. Belt Friction 92
40. Rolling Friction and Pivot Friction 94

Chapter 7. Couples and Forces in Space

41. Moment of a Force About a Point as a Vector 95
42. Moment of a Force with Respect to an Axis 97
43. Relation Between the Moments of a Force about a Point and an Axis 100
44. Vector Expression of the Moment of a Couple 101
45. Composition of Couples in Space. Conditions of Equilibrium of Couples 101
46. Reduction of a Force System in Space to a Given Centre 104
47. Reduction of a Force System in Space to the Simplest Possible Form 106
48. Condition of Equilibrium of an Arbitrary Force System in Space. The Case of Parallel Forces 108
49. Varignon’s Theorem of the Moment of a Resultant with Respect to an Axis 109
50. Problems on the Equilibrium of Bodies Subjected to the Action of Force Systems in Space 110
51. Conditions of Equilibrium of a Constrained Rigid Body. Concept of Stability of Equilibrium 117

Chapter 8. Centre of Gravity

52. Centre of Parallel Forces 118
53. Centre of Gravity of a Rigid Body 120
54. Coordinates of Centres of Gravity of Homogeneous Bodies 122
55. Methods of Determining the Coordinates of the Centre of Gravity of Bodies 122
56. Centre of Gravity of Some Homogeneous Bodies 125

PART 2. KINEMATICS OF A PARTICLE AND A RIGID BODY

Chapter 9. Rectilinear Motion of a Particle

57. Introduction to Kinematics 128
58. Equation of Rectilinear Motion 129
59. Velocity and Acceleration of a Particle in Rectilinear Motion 130
60. Some Examples of Rectilinear Motion of a Particle 132
61. Graphs of Displacement, Velocity and Acceleration of a Particle 134
62. Solution of Problems 138

Chapter 10. Curvilinear Motion of a Particle

63. Vector Method of Describing Motion of a Particle 137
64. Velocity Vector of a Particle 138
65. Acceleration Vector of a Particle 130
66. Theorem of the Projection of the Derivative of a Vector 141
67. Coordinate Method of Describing Motion. Determination of the Path, Velocity and Acceleration of a Particle 142
68. Natural Method of Describing Motion. Determination of the Velocity of a Particle 147
69. Tangential and Normal Acceleration of a Particle 148
70. Some Special Cases of Particle Motion 151
71. Velocity in Polar Coordinates 156
72. Graphical Analysis of Particle Motion 156

Chapter 11. Translatory and Rotational Motion of a Rigid Body

73. Motion of Translation 160
74. Rolatiotral Atotion of a Rigid Body. Angular Velocity and Angular Acceleration 162
75. Uniform and Uniformly Variable Rotation 164
76. Velocities and Accelerations of llie Points of a Rotating Body 166

Chapter 12. Plane Motion of a Rigid Body

77. Equations of Plane Motion. Resolution of Motion into Translation and Rotation 170
78. Determination of the Paths of the Points of a Body 172
79. Determination of the Velocity of Any Point of a Body 173
80. Theorem of the Projections of the Velocities of Two Points of a Body 174
81. Determination of the Velocity of Any Point of a Body Using the
Instantaneous Centre of Zero Velocity 175
82. Solution of Problems 178
83. Velocity Diagram 182
84. Determination of the Acceleration of Any Point of a Body 184
85. Instantaneous Centre of Zero Acceleration 191

Chapter 13. Motion of a Rigid Body Having One Fixed Point and Motion of a Free Rigid Body

86. Motion of a Rigid Body Having One Fixed Point 193
87. Acceleration of Any Point of a Body 195
88. The Most General Motion of a Free Rigid Body 196

Chapter 14. Resultant Motion of a Particle

89. Relative, Transport, and Absolute Motion 198
90. Composition of Velocities 200
91. Composition of Accelerations. Coriolis Theorem 203
92. Calculation of Coriolis Acceleration 207
93. Solution of Problems 207

Chapter 15. Resultant Motion of a Rigid Body

94. Composition of Translatory Motions 215
95. Composition of Rotations About Two Parallel Axes 215
96. Toothed Spur Gearing 218
97. Composition of Rotations About Two Intersecting Axes 221
98. Composition of a Translation and a Rotation. Screw Motion. 223

PART 3. PARTICLE DYNAMICS

Chapter 16. Introduction to Dynamics, Laws of Dynamics

99. Basic Concepts and Definitions 226
100. The Laws of Dynamics 227
101. Systems of Units 230
102. The Problems of Dynamics for a Free and a Constrained Particle 230
103. Solution of the First Problem of Dynamics 231

Chapter 17. Differential Equations of Motion for a Particle and Their Integration

104. Rectilinear Motion of a Particle 233
105. Solution of Problems 236
106. Body Falling in a Resisting Medium (in Air) 241
107. Curvilinear Motion of a Particle 244
108. Motion of a Particle Thrown at an Angle to the Horizon in a Uniform Gravitational Field 245

Chapter 18. General Theorems of Particle Dynamics

109. Momentum and Kinetic Energy of a Particle 248
110. Impulse of a Force 249
111. Theory m of the Change in the Momentum of a Parlicie 250
112. Work Done by a Force. Power 251
113. Examples of Calculation of Work 254
114. Theorem of the Change in the Kinetic Energy of a Particle 256
115. Solution of Problems 258
116. Theorem of the Change in the Angular Momentum of a Particle (the Principle of Moments) 264

Chapter 19. Constrained Motion of a Particle and D’Alembert’s Principle

117. Equations of Motion of a Particle Along a Given Fixed Curve 268
118. Determination of the Reactions of Constraints 270
119. D’Alembert’s Principle 272

Chapter 20. Relative Motion of a Particle

120. Equations of Relative Motion and Rest of a Parlicie 275
121. Effect of the Rotation of the Earth on the Equilibrium and Motion of bodies 278
122. Deflection of a Falling Particle from the Vertical by the Earth’s
Rotation 281

Chapter 21. Vibration of a Particle

123. Free Harmonic Motion 284
124. The Simple Pendulum 288
125. Damped Vibrations
126. Forced Vibrations. Resonance 291

Chapter 22. Motion of a Body In the Earth’s Gravitational Field

127. Motion of a Particle Thrown at an Angle to the Horizon In the Earth’s Gravitational Field 299
128. Artificial Earth Satellites. Elliptical Paths 304

PART 4. DYNAMICS OF A SYSTEM AND A RIGID BODY

Chapter 23. Introduction to the Dynamics of a System. Moments of Inertia of Rigid Bodies

129. Mechanical Systems. External and Internal Forces 308
130. Mass of a System. Centre of Mass 309
131. Moment of inertia of a Body About an Axis. Radius of Gyration 310
132. Moments of Inertia of Some Homogeneous Bodies 311
133. Moments of Inertia of a Body About Parallel Axes. The Parallel-Axis (Huygens’) Theorem 313

Chapter 24. Theorem of the Motion of the Centre of Mass of a System

131. The Differential Equations of Motion of a System 315
135. Theorem of the Motion of Centre of Mass 316
136. The Law of Conservation of Motion of Centre of Mass 317
137. Solution of Problems 319

Chapter 25. Theorem of the Change in the Linear Momentum of a System

138. Linear Momentum of a System 323
139. Theorem of the Change in Linear Momentum 324
140. The Law of Conservation of Linear Momentum 325
141. Solution of Problems 326
142. Bodies Having Variable Mass. Motion of a Rocket 329

Chapter 26. Theorem of the Change In the Angular Momentum of a System

143. Total Angular Momentum of a System 332
144. Theorem of the Change in the Angular Momentum of a System
(Ihe Principle of Moments) 333
145. The Law of Conservation of the Total Angular Momentum 334
146. Solution of Problems 337

Chapter 27. Theorem of the Change In the Kinetic Energy of a System

147. Kinetic Energy of a System 339
148. Theorem of Ihe Change in the Kinetic Energy of a System 344
149. Some Cases of Computation of Work 316
150. Solution of Problems 318
151. Field of Force. Potential Energy 353
152. The Law of Conservation ol Mechanical Energy 355

Chapter 28. Some Cases of Rigid-Body Motion

153. Rotation of a Rigid Body 355
154. The Compound Pendulum 359
155. Determination of Moments ol Inertia by Experiment 361
156. Plane Motion of a Rigid Body 361
157. Approximate Theory of Gyroscopic Action 368

Chapter 29. D’Alembert’s Principle. Forces Acting on the Axis ol a – y r Rotating Body

158. D’Alembert’s Principle for a System 373
159. The Principal Vector and the Principal Moment of the Inertia
Forces of a Rigid Body 374
160. Solution of Problems 376
161. Dynamical Pressures on the Axis til a Rotating Body 380
162. The Principal Axes of Inertia of a Body. Dynamic Balancing of Masses 382

Chapter 30. The Principle of Virtual Work and Ihe General Equation of Dynamics

163. Virtual Displacements of a System. Degrees of Freedom 386
164. Idea] Constraints 388
165. The Principle of Virtual Work 368
166. Solution of Problems 390
167. The General Equation of Dynamics 395

Chapter 31. The Theory of Impact

168. The Fundamental Equation of Ihe Theory of Impact 398
169. General Theorems of Ihe Theory of Impact 400
170. Coefficient of Restitution 401
171. Impact of a Body Against a Fixed Obstacle 403
172. Direct Central Impact of Two Bodies (Impact of Spheres) 405
173. Loss of Kinetic Energy in Perfectly Inelastic Impact. Carnot’s Theorem 407
174. Impact with a Rotating Body 409

Name Index 414
Subject Index 414 