In this post, we will see the book Theoretical Mechanics by M. Movnin; A. Izrayelit.
About the book
The new international system of units (SI) is used throughout the text. However, taking into account that the engineers’ system (mkgfs) still finds wide use, the units of this system are also given. Moreover, wherever necessary the relations are indicated between the units of the international and engineers’ systems. Normative and design data are given in both systems of units.
In the presentation of the material primary emphasis is placed on the practical significance of conclusions.
To gain a better understanding of theoretical propositions, the solutions of sample problems are given. All solutions are first carried out in algebraic form and then numerical data are substituted.
Although the book is mainly intended for full-time vocational schools, the large number of detailed and specially selected examples makes it handy for their evening and correspondence departments as well.
The book was translated from Russian by M. Konyaeva was published in 1970 by Mir Publishers.
You can get the book here.
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Contents
From the Authors 5
Notation 12
Introduction 15
Chapter I. Basic Definitions and Axioms of Statics 17
1. Fundamentals 17
2. Axioms of Statics 22
3. Constraints and Their Reactions. Axioms of Constraints 25
Chapter II. Systems of Concurrent Forces in a Plane 28
4. Analytic Determination of the Resultant of Two Forces Applied at the Same Point 28
5. Resolution of a Force into Two Components Applied at the Same Point 30
6. Point Addition of Concurrent Forces in a Plane. Force Polygon 32
7. Projection of a Force on an Axis 33
8. Projection of a Vector Sumon an Axis 36
9. Analytic Determination of the Resultant of a System of Concurrent Forces (Method of Projections) 37
10. Conditions and Equations of Equilibrium for a System of Concurrent Forces 39
11. Procedure for Solving Equilibrium Problems 40
12. Theorem of Concurrence of Three Mutually Balanced Non-Parallel Forces 49
Chapter III. Couple 52
13. Addition of Two Parallel Forces of the Same Sense 52
14. Addition of Two Parallel Forces of OppositeSense 53
15. Moment of a Couple 56
16. Equivalence of Couples. Translation of a Couple in Its Plane of Action 58
17. Theorem of Equivalent Couples 60
18. Addition of Couples Acting in the Same Plane 61
Chapter IV. Two-Dimensional Systems of Arbitrarily Located Forces 65
19. Moment of a Force About a Point 65
20. Equilibrium of a Lever 67
21. Reduction of a Force to a Given Point 69
22. Reduction of a Two-Dimensional Force System to a Given Point 70
23. Resultant of a Two-Dimensional Force System 72
24. Theorem of the Moment of a Resultant (Varignon’s Theorem) 73
25. A Case of the Reduction of a Two-Dimensional Force System to a Couple 79
26. Conditions and Equations of Equilibrium for a Two-Dimensional Force System 80
27. Three Forms of Equilibrium Equations 82
28. Supporting Devices of Beam Systems 85
29. Classification of Loads 88
30. Practical Solution of Equilibrium Problems for Two-Dimensional Force Systems 89
31. Equilibrium of a System of Connected Bodies 101
Chapter V. Friction 106
32. Types of Friction 106
33. The Laws of Sliding Friction 107
34. Angle and Cone of Friction 109
35. Experimental Determination of Coefficients of Friction 114
36. The Laws of Rolling Friction 116
Chapter VI. Three-Dimensional Force Systems 120
37. Force Parallelepiped 120
38. Equilibrium of a System of Concurrent Forces in Space 121
39. Moment of a Force About an Axis 123
40. Equilibrium of an Arbitrary Three-Dimensional Force System 128
Chapter VII Centroids and Centres of Gravity 134
41. Centre of Parallel Forces 134
42. Co-ordinates of the Centre of ParallelForces 135
43. Centroid of a Volume 139
44. Centroid of an Area. Static Moments of an Area 141
45. Centroid of a Line 147
46. Stability of Equilibrium 147
PART 2. KINEMATICS
Chapter VIII. Fundamentals 154
47. Subject of Kinematics 154
48. Space and Time 154
49. Basic Definitions 156
Chapter IX. Kinematics of Particles 160
50. Methods of Specifying the Motion of a Particle 160
51. Velocity of a Particle 162
52. Acceleration of a Particle 167
53. Types of Motion of a Particle as Related to Acceleration 174
54. Uniformly Variable Motion of a Particle 176
55. Kinematic Graphs and Relationship Between Them 180
Chapter X. Simple Motions of Rigid Bodies 185
56. Translation of a Rigid Body 185
57. Rotation of a Rigid Body About a Fixed Axis 186
58. Velocities and Accelerations of Points of a Rotating Body 191
Chapter XI. Methods of Transmission of Rotary Motion 198
59. Classification of Transmission Mechanisms 198
60. Gear Ratio 198
61. Cylinder Friction Drives 200
62. Face Friction Drives 202
63. Cone Friction Drives 203
64. Belt Drives: Fundamental Concepts 205
65. Gear Drives: General Considerations 206
66. Gear Ratio of a Spur Gear Drive 207
67. Gear Trains 208
68. Worm Gearing 212
Chapter XII Complex Motion of Particles 216
69. Base, Relative and Absolute Motions 216
70. Theorems on Addition of the Velocities and Accelerations of a Particle in Complex Motion 219
Chapter XIII. Plane Motion. 225
71. Concept of Plane Motion of a Rigid Body 225
72. Determination of the Velocity of Any Point of a Body in Plane Motion 226
73. Instantaneous Centre of Zero Velocity 228
74. Determination of the Acceleration of Any Point of a Body in Plane Motion 240
75. Planetary Gearing 244
76. Differential Gearing 247
PART 3. DYNAMICS
Chapter XIV Basic Concepts and Axioms of Dynamics 251
77. Subject of Dynamics 251
78. Principle of Inertia 252
79. Fundamental Law of Dynamics of Particles 252 80. Systems of Units 254
81. Axiom of Superposition 256
82. Axiom of Interaction 258
83. Two Basic Problems of Dynamics 259
Chapter XV. Motion of Particles. Method of Kinetostatics 268
84. Ideal and Real Constraints 268
85. D ’Alembert’s Principle 269
86. Inertia Force for a Particlein Rectilinear Motion 271
87. Inertia Force for a Particle in Curvilinear Motion 271
88. Inertia Force for a Rigid Body 274
89. Solution of Problems by the Method of Kinetostatics 275
Chapter XVI Work and Power 280
90. Work of a Constant Force in Rectilinear Motion 280
91. Work of a Variable Force in Curvilinear Motion 282
92. Work of a Resultant Force 283
93. Work of a Force of Gravity 285
94. Work of an Elastic Force 286
95. Concept of Mechanical Efficiency 289
96. Efficiency of a System of Mechanisms Connected in Series 290
97. Efficiency of a System of Mechanisms Connected in Parallel 291
98. Power 296
99. Work and Efficiency for Bodies Sliding Along an Inclined Plane 298
100. Work and Power in Rotation 306
101. Work in Rolling Motion 308
Chapter XVII The Laws of Dynamics 315
102. Concept of a System of Particles 315
103. Law of Momentum for a Particle 317
104. Law of Momentum for a System of Particles 322
105. Potential and Kinetic Energy 324
106. Kinetic Energy of a Body in Various Types of Motion 325
107. Moments of Inertia of Homogeneous Bodies of Simple Shape 327
108. Law of Kinetic Energy for a Particle 330
109. Law of Kinetic Energy for a System of Particles 333
110. Fundamental Equation of Dynamics for a Rigid Body in Rotation 338
Chapter XVIII. Application of the Laws of Kinematics and Dynamics to the Analysis to Mechanisms 345
111. Principles and Definitions 345
112. Fundamentals of Kinematics of Mechanisms 350
113. Examples of Constructing Velocity Diagrams 359
114. Distribution of Accelerations in a Body in Plane Motion 363
115. Examples of Constructing Acceleration Diagrams 367
116. Cam Gears 374
117. Introduction to the Dynamics of Machinery 381
118. Fundamentals of the Dynamic Analysis of Mechanisms 387
119. Fundamentals of Regulation. 395
Subject Index 406
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