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

## About the book

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