PREFACE 11

PART I. THEORETICAL MECHANICS I 15

 Chapter 1: Introduction 17

Lecture1

1.1. What is Mechanics? 17

1.2. Classification of Mechanics 17

1.3. Historical outline 19

1.4. Mechanics as a theory 20

1.5. Parts of Mechanics 22

1.6. Mechanical quantities and system of physical units 22

1.7. Useful knowledge preceding Mechanics 23

Review questions to Chapter 1 24

Chapter 2: Vectors and vector calculus 25

Lecture 2

2.1. Scalars and vectors in Mechanics 25

2.2. Geometric and analytic description of vectors 25

2.3. Vector calculus 26

2.4. Vector functions of time 29

Review questions to Chapter 2 34

Chapter 3: Geometry of masses 35

Lecture 3

3.1. What is geometry of masses? 35

3.2. First moments and center of mass of a multi-particle system and a body 36

3.3. Calculation of first moments and positions of mass centers of bodies 38

3.4. Pappus-Guldinus rules 46

Lecture  4

3.5. Moments and products of inertia (second moments) 49

3.6. Calculation of second moments 53

3.7. Transformation of the second moments due to translation of reference frame 58

Lecture 5

3.8. Transformation of second moments due to rotation of the reference frame 64

3.9. Principal axes and principal moments of inertia 68

3.10. Ellipsoid of inertia of a body at a point 73

Review questions to Chapter 3 76

Chapter 4: Statics of mecha nical systems 77

Lecture 6

4.1. Subject, problems and methods of statics 77

4.2. Classification of forces (and free moments) in statics 80

4.3. Constraints and supports of mechanical systems 82

4.4. Equivalent reduction of forces and moments acting on a body 84

4.5. Geometric conditions of equilibrium of mechanical systems 92

Lecture 7

4.6. Friction in statics of mechanical systems 96

4.7. Friction-induced zones of equilibrium and intervals of loads 98

4.8. Friction-induced static indeterminability 101

4.9. Duality of loss of equilibrium 102

4.10. Self-locking and jamming effects 108

Lecture 8

4.11.  Rolling resistance 114

4.12. Belt friction 117

4.13. Plane trusses 119

Review questions to Chapter 4 125

Chapter 5: Kinematics of a particle 127

Lecture 9

5.1. Geometric and analytic description of position of a particle 127

5.2. Path of a particle in space 129

5.3. Velocity and acceleration of a particle 135

5.4. Components of velocity and acceleration in the cylindrical reference frame 137

Lecture 10

5.5. Components of velocity and acceleration in natural directions 141

5.6. Rectilinear motion of a particle 144

5.7. Curvilinear motion of a particle in a uniform field of acceleration 149

5.8. Motion of a particle in a central field of acceleration 150

Review questions to Chapter 5 152

Chapter 6: Dynamics of a particle 153

Lecture 11

6.3. Motion of a particle under force dependent on position 155

6.4. Motion of a particle under force dependent on velocity 162

Lecture 12

6.6. Motion of a particle under force dependent on time 169

6.7. Dynamics of a constrained particle 171

6.8. Linear momentum law of a particle 175

6.9. Angular momentum law of a particle 179

Lecture 13

6.10. Work and power of a force acting on a particle 183

6.11. Kinetic energy of a particle and kinetic energy law 186

6.12. Kinetic energy law in a potential field of force 188

Review questions to Chapter 6 194

Chapter 7: Dynamics of multi-particle systems 195

Lecture 14

7.1. Definition and basic properties of a multi-particle system 195

7.2. Equations of motion of a multi-particle system 198

7.3. Linear momentum law of a multi-particle system 203

7.4. Law of motion of the mass center of a multi-particle system 205

Lecture 15

7.5. Angular momentum law of a system of particles 210

7.6. Kinetic energy law of a system of particles 213

7.7. Kinetic energy law in case of potential forces 215

Review questions to Chapter 7 222

PART II. THEORETICAL MECHANICS II 223

Chapter 8: Kinematics of a rigid body 225

Lecture 1

8.1. Description of the position of a body in space 225

8.2. Classification of motions of a rigid body 231

8.3. Velocity of points of a body in arbitrary motion 233

Lecture 2

8.4. Acceleration of points of a body in arbitrary motion 236

8.5. Velocity and acceleration of points of a body in translatory motion 240

8.6. Velocity and acceleration of points of a body in rotation about a fi xed point 242

Lecture 3

8.7. Velocity and acceleration of points of a body in plane motion 248

8.8. Velocity and acceleration of points of a body in screw motion 256

Review questions to Chapter 8 258