About the book

This general course of Mechanics by late Prof. S. P. Strelkov is meant for students of Physical and Mathematical Departments of Universities and pedagogical colleges. It is based on the material of the seminars and lectures given by the author for many years at the Physics Department of the State University of Moscow.

The present book is the revised translation of the 1975 Russian edition in which the course was considerably remade and enlarged. This first of all concerns such important divisions of mechanics as dynamics of a rigid body, theory of deformable bodies, hydrodynamics, and relativistic dynamics. The pedagogical skill of the author makes the presentation of the fundamentals of mechanics extremely clear and visual. The book includes many important and instructive examples covering a wide range of mechanical phenomena. The book can serve as an introduction to practical and theoretical physics.

Contents

Foreword to the Third Russian Edition

Introduction

PART ONE

Mechanics of Rigid Bodies

Chapter 1: Kinematics of a Particle

1. Motion of Bodies

2. Rectilinear Motion of a Particle

3. Velocity of a Particle in Rectilinear Motion

4. Relationship between the Velocity and the Distance Travelled

5. Acceleration of a Particle in Rectilinear Motion

6. Three-dimensional Motion of a Particle

7. Basic Properties of Vectors

8. Velocity of a Particle

9. Acceleration of a Particle in Plane Motion. Centripetal Acceleration

10. Acceleration of a Particle in Three-dimensional Motion

11. Space, Time, and Frames of Reference

Chapter 2: Fundamental Laws of Dynamics

12. Motion and Interaction of Bodies

13. Force

14. Measuring Constant Forces

15. Equilibrium Conditions for Forces Acting on a Particle

16. Force and Motion (Newton’s First Law)

17. Newton’s Second Law

18. Mass of a Body

19. General Form of Newton’s Second Law

20. Newton’s Third Law

21. Forces and Newton’s Second and Third Laws

22. Motion of a Body under the Action of Given Forces

23 Constrained Motion of a Body

Chapter 3: Momentum of a System of Bodies

24. Law of Conservation of Momentum

25. Transfer of Momentum from One Body to Another

26. Impulse of a Force

27. Motion of a Body with Variable Mass

Chapter 4: Work and Energy

28. The Concept of Energy

29. Work and Energy

30. Work of a Force

31. Potential Energy of Strain

32. Kinetic Energy of a Body

33. Perfectly Plastic Impact of Two Bodies

34. Elastic Impact

35. Impact of Non-elastic Bodies

36. Potential Energy

37. Change of Energy of a Body in the Gravitation Field. Law of Conservation of Energy

Chapter 5: Friction

38. Various Types of Friction Forces

39. Viscous Friction

40. Fall of a Ball in a Viscous Medium

41. Dry Friction

42. Force of Sliding Friction

Chapter 6: Relative Motion

43. Inertial Reference Frames

44. Motion of a Body in a Non-inertial System of Reference. Inertia Forces

45. Inertia Forces Acting on a Body in a Rotating Frame of Reference

46. Weightlessness

47. The Relationship between the Vectors of Angular and Linear Velocities of a Particle

48. Inertia Forces Acting on a Body Moving in a Rotating Frame of Reference

49. The Influence of the Earth’s Rotation on the Motion of Bodies. The Foucault Pendulum

Chapter 7: Motion of a Rigid Body

50. Translatory and Rotational Motions of a Rigid Body 1

51. Equilibrium Conditions for a Rigid Body with a Fixed Axis of Rotation

52. Law of Dynamics for a Body Rotating About a Fixed Axis

53. Angular Momentum

54. Kinetic Energy of a Rotating Body

55. Centre of Gravity and Centre of Mass of a Rigid Body

56. The Law of Motion of the Centre of Mass of a Body

57. Plane Motion of a Body

58. Rolling Motion of a Cylinder on a Plane. Maxwell’s Pendulum

59. Moments of Inertia of Some Bodies. Huygens-Steiner Parallel Axes Theorem

60. Kinetic Energy of a Body for Simultaneous Translatory and Rotational Motions

61. Free Axes of Rotation

62. Kinematics of a Rigid Body

63. Moment of a Force About a Point and Angular Momentum of a Rigid Body

64. Angular Momentum of a Rigid Body and Moment of Inertia

65. The Fundamental Law of Dynamics of a Rigid Body

66. Gyroscopes

67. Motion of the Axis of a Gyroscope

68. Gyroscopic Effect

69. Rotation of the Axis of a Constrained Gyroscope

70. Motion of a Free Gyroscope

71. On Gyroscopic Forces

Chapter 8: Rolling Friction

72. Forces of Rolling Friction. Forces of Sliding Friction in Rolling Motion of a Cylinder

73. Adhesion of Wheels

74. Braking and Skidding

75. Rolling Friction

Chapter 9: Gravitational Attraction of Bodies

76. Law of Universal Gravitation

77. Inertial Mass and Gravitational Mass

78. Potential Energy of Gravitation

79. Basic Laws of Celestial Mechanics

80. Motion of Earth’s Satellites and Spaceships

PART TWO

Mechanics of Deformable Bodies

Chapter 10: Mechanics of Deformable Solids

81. The Concept of an Elastic Body, Forces and Deformations in Tension

82. Physical Phenomena in a Deformable Body. Properties of Materials

83. Internal Forces and Stresses

84. Shearing Stresses and Strains

85. Stresses in an Elastic Body. General Case

86. Small Deformations of a Body

87. Relationship Between Stresses and Strains

88. Strain Energy

89. Forces and Deformations in the Bending of Beams

90. Determination of Deflection of a Beam

91. On Deformation of Supports

92. Stresses in Overload and Weightlessness

Chapter 11: Equilibrium of Fluids and Gases

93. Solids, Fluids, and Gases

94. The Concept of Pressure

95. Relationship Between the Density of a Gas and the Pressure

96. Distribution of Pressure in a Fluid in Equilibrium State

97. Distribution of Pressure in a Gas

98. Equilibrium of Bodies Floating on the Surface of a Fluid

99. Equilibrium Conditions for a Body Immersed in a Fluid or Gas

Chapter 12: Motion of Fluids and Gases

100. Stationary Fluid Flow

101. Fundamental Law of Dynamics for a Particle of an Ideal Fluid

102. Bernoulli’s Equation for a Stationary Flow of an Incompressible Fluid

103. Outflow of a Heavy Fluid from a Vessel

104. Pressure in Fluid Flow in a Pipe with Variable Cross Section

105. Outflow of Fluid or Gas from a Vessel Under the Action of Pressure

106. Pressure at the Stagnation Point in a Flow Around a Body

107. Variation of Pressure Across a Stream Tube

108. Distribution of Pressure in a Rotating Fluid

109. Momentum of Fluid or Gas

110. Reaction Force of Flowing Fluid

111. Flow of a Viscous Fluid in a Pipe

Chapter 13:Action of a Fluid or Gas Flow on a Body

112. Drag Force

113. Dynamical Similarity of Bodies

114. Boundary Layer

115. Measuring Forces Acting on a Body in a Flow of Fluid or Gas

116. Lift Force of a Wing of an Airplane

117. Fluid Flow Around a Wing. Circulation. Lift Force

118. Dependence of the Lift Force on the Angle of Incidence. Wing Drag

119. Forces in a Flight of an Airplane

120. Propagation of Pressure Disturbances in a Compressible Fluid. Supersonic Motion of a Body

121. Wave with Large Variation of Pressure. Motion of a Body with Large Velocity

122. Supersonic Flow in a Pipe

PART THREE

Oscillations and Waves. Elements of Acoustics.

Fundamentals of Special Theory of Relativity

Chapter 14: Oscillations

123. Periodic Processes

124. Harmonic Vibrations

125. Natural Oscillation and Variation of Energy in Oscillation Process

126. Damped Natural Oscillations

127. Forced Oscillation and Resonance

128. Dependence of the Amplitude of a Forced Oscillation on the Frequency

129. Vibration of a Shaft with Disk

130. Transient Processes and Compound Vibrations. Harmonic Analysis

131. Auto-oscillation

132. Natural Oscillations of a System with Many Degrees of Freedom

133. Theoretical Analysis of Beating

134. Natural Frequencies of Coupled Pendulums

135. Natural Frequencies of Three Connected Pendulums

136. Forced Oscillations in Composite Systems

Chapter 15: Vibrations in a Continuous Medium

137. Waves

138. Sinusoidal Plane Sound Wave

139. Energy of Sound Wave

140. Plane Waves in a Gas and in a Homogeneous Elastic Medium

141. Superposition (Interference) of Waves

142. Reflection of Waves

143. Natural Vibrations of a String and of the Air in a Pipe

Chapter 16: Elements of Acoustics

144. Basic Phenomena

145. Reflection of Sound Waves

146. Propagation of Sound Waves

147. Hearing

148. Ultrasonic Vibrations

Chapter 17: Fundamentals of Special Theory of Relativity

149. Galileo’s Principle of Relativity

150. Constancy of Speed of Light

151. Simultaneity of Events

152. Lorentz Transformation

153. Analysis of Lorentz Transformation

154. Momentum

155. Dependence of Mass on Velocity of Motion

156. Transformation Laws for Momentum and Mass

157. Energy

158. Momentum and Energy of System of Particles

159. Invariants

160. Four-vector. Space-like, Time-like, and Light-like Intervals

161. Relativistic Mechanics

162. Theory of Elastic Impact of Two Particles

Name Index

Subject Index