Folktales of the Soviet Union – The Baltic Republics

In this post. we will see the book Folktales of the Soviet Union – The Baltic Republics compiled by Robert Babloyan and Mirlena Shumskaya.

About the book

The book is a collection of folk tales from the Baltic region. The Soviet Baltic republics, Latvia, Lithuania and Lstonia, are closely bound up with the sea. And the people who live there are what you would expect sea tolk to be, tall, tough and strong. This is a land of fishermen, ship-builders and farmers. Lach republic also has a highly developed industry. The radios, transmitters, etc. made in Latvia and Estonia are known throughout the world.

Baltic folk tales have absorbed much of the world around them, of course. They seem to smell of dry wood, resin, sea and forest. Many of the characters in the old songs and legends resemble the people of today who live in these parts: the wise fishermen, the skilled craftsmen, the sturdy, brave young men and the gentle, faithful women. The forces of evil in these stories take the form of terrible monsters, catastrophies and disasters which the heroes have to combat and overcome.

The book was translated from the Russian by and was published by Raduga in 1986.

The book has some amazing full page paintings, done by three different artists one for each set of the tales: Gunars Krollis for Lativia, Jaan Tammsaar for Estonia and Vange Gedmantaitc-Galkuviene for Lithuania. The book was designed by Mikhail Anikst.



The Internet Archive Link




The White Deer 6

The Sea Bride 26


The King of the Mushrooms 48

The Forbidden Knot 72


The Sun Princess and the Prince 96

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Strength of Materials – Kinasoshvili

In this post, we will see the book Strength of Materials by R. Kinasoshvili.

Kinasoshvili - Strength of Materials - Mir - 1978_0000

A book covering various aspects of strength of materials. The topics covered are succinct and with basic definitions and requisite mathematics. Each chapter has a set of “Check Questions” in the end.

The development of the foundations for the design of structural members is the subject matter of a science called the strength of ma­terials.

Without knowledge of the fundamentals of strength of materials it is impossible to construct even a simple machine satisfying the technical requirements placed on each construction.

The book was translated from the Russian by M. Konyaeva and was published by Mir in 1978 (second print).

Many thanks to Akbar Azimi for the raw scans.

The Internet Archive Link


Introduction. 13

1. Science of Strength of Materials. Concepts of Deformation and of an Elastic Body 13
2. Classification of External Forces 16
3. Basic Types of Deformation 17
4. Method of Sections. Stress 19
5. Check Questions 22

Chapter II. Tension and Compression 23
6. Longitudinal Strain. Stress. Hooke’s Law 23
7. Lateral Strain in Tension and Compression 27
8. Experimental Study of Materials in Tension 29
9. Tension Test Diagram and Its Characteristic Points 31
10. Strain Hardening 38
11. Strain Energy in Tension 40
12. Compression Testing 42
13. Harness 43
14. Check Questions 45

Chapter III. Strength Design for Tension and Compression 47

15. Allowable Stress and Selection of Sections 47
16. Effect of Gravity in Tension and Compression 54
17. Stepped Rod 57
18 Statically Indeterminate Problems in Tension and Compression 60
19. Stresses Due to Temperature Changes 65
20. Design of Statically Indeterminate Systems Based on Allowable Loads, and Limit Design 68
21. Check Questions 74

Chapter IV. Combined Stresses

22. Stresses on Inclined Sections Under Axial Tension or Compression
23. Concept of Principal Stresses
24. Stresses on Inclined Sections Under Tension (Compression) in Two Mutually Perpendicular Directions 79
25. Determination of Principal Stresses 81
26. Strains Under Tension or Compression in Two Mutually Perpendi­cular Directions. Strain Energy 84
27. Strength Theories 87
28. Design of Thin-Walled Vessels 94
29. Check Questions 98

Chapter V. Shear 99
30. Concept of Shear. Stresses in Shear. Hooke’s Law in Shear 99
31. Pure Shear in a Rod Subjected to Tension and Compression in Two Mutually Perpendicular D irections 101
32. Relation Between Moduli of Elasticity E and G 102
33. Allowable Stress in Shear 104
34. Crushing 106
35. Examples of Design for Shear andCrushing. 107
36. Design of Welded Joints 111
37. Check Questions. 114

Chapter VI. Torsion 116

38. Construction of Twisting Moment Diagrams. Relation Between Torque. Power and Number of Revolutions 116
39. Determination of Stresses and Strains in a Circular Bar Subjected to Torsion 121
40. Polar Moment of Inertia and Section Modulus of a Circle and a Cir­cular Ring 126
41. Design Equations in Torsion 128
42. Elements of Design of Bars of Rectangular Section for Torsional Loads 136
43. Potential Energy in Torsion 139
44. Design of Closely Coiled Helical Springs 140
45. Design of Shafts Based on Allowable Loads 142
46. Check Questions 144

Chapter VII. Static Moments, Centroids and Moments of Inertia of Plane Figures 145

47. Static Moments of Plane Figures 145
48. Moments of Inertia of Plane Figures 148
49. Transformation Formulas for Moments of Inertia in the Case of Pa­rallel Transfer of Axes 149
50. Moments of Inertia of Some Simple Figures 151
51. Determination of Moments of Inertia of Figures Composed of Simple Figures 155
52. Transformation Formulas for Moments of Inertia in the Case of Rotation of Axes 157
53. Concept of Principal Axes of Inertia and Determination of Their Position 160
54. Determination of Principal Moments of Inertia 163
55. Check Questions 167
Chapter VIII. Bending of a Straight Rod, Bending Moment and Shearing Force 168

56. General Considerations 168
57 Supports and Reactions at Supports of Beams 171
58. Determination of Reactions at Supports of Beam 173
59 Shearing Force and Bending Moment 176
60. Relations Between Load Intensity, Shearing Force and Bending Moment 178
61. Construction of Bending Moment and Shearing Force Diagram? 179
62. Check Questions 197

Chapter IX. Stresses in Bending and Design of Beams for Strength 198

63. Determination of Normal Stresses in Bending 198
64. Section Moduli for Common Sections 198
65. Design Flexure Formulas. Examples of Designing Beams 204
66. Shearing Stresses in a Beam of Rectangular Section. Jourawski’s Formula 211
67. Shearing Stresses in an I-Beam 216
68. Verification of the Strength of a Beam on the Basis of Principal Stresses 218
69. Design of Beams Based on Allowable Loads, and Limit Design 221
70. Check Questions 224

Chapter X The Elastic Curve of a Beam 226

71. The Elastic Curve of a Beam 226
72 Derivation of the Generalized Equation of the Elastic Curve 230
73. Special Cases of Determining Displacements of Beams from the Ge­neralized Equation of the Elastic Curve 233
74. Mohr’s Method and Vereshchagin’s Rule 241
75. Beams of Uniform Resistance to Bending 246
76. Check Questions 252

Chapter XI. Statically Indeterminate Beams 253

77. Concept of Statically Indeterminate Beams 253
78. A Beam Fixed at One End and Simply Supported at the Other 253
79. A Beam with Both Ends Fixed 259
80. A Beam on Three Supports 263
81. Check Questions 268

Chapter XII Complex Resistance 269

82. Oblique Bending 269
83. Bending Combined with Tension or Compression 276
84. Eccentric Compression 278
85. The General Case of Eccentric Compression or Tension. 279
86. Concept of Core of Section. 282
87. Combined Bending and Torsion. 284
88. Combined Torsion and Tension or Compression 290
89. Check Questions 291
Chapter XIII. Buckling 292

90. Concept of Buckling. 292
91. Euler’s Formulas 294
92. Limitations of Euler’s Formulae able for Column Design 298
93. Examples of Design for Buckling Strength. 300
94. Check Questions. 306

Chapter XIV. Strength Under Dynamic and Repeated Loading 307

95. Concepts of Dynamic and Repeated Loading 307
97. The Stress and Strain in a Rod Subjected to Impact Loading 308
96. Design of a Uniformly 310
98. Impact Testing of Metals 313
99. Fatigue of Metals 314
100. Fatigue Testing of Materials 317
101. Endurance Limit for Fluctuating Stress Cycle 320
102. Effect of Overall Dimensions of Parts on Endurance Limit 321
103. Strength Design for Completely Reversed Stresses 323
104. Determination of Factor of Safety in the Case of Fluctuating Stresses 326
105. Construction of Approximate Fatigue Strength Diagram and Deter­mination of Factor of Safety from It 328
106. Determination of Factor of Safety in the Case of Combined Varying 336 Stresses 336
107. Examples of Design for Varying Stresses 336
108. Improvement of Fatigue Strength 338
109. Check Questions 341

Appendices 343
Index 356

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Manual of the Theory of Elasticity – Rekach

In this post, we will see the book Manual of the Theory of Elasticity by V. G. Rekach.

Rekach - Manual of the Theory of Elasticity - Mir - 1979_0000

About the book

This book is designed to be used as an aid to solving elasticity problems in college and university courses in engineering.
The book covers all subjects of the mathematical theory of elasticity. It contains material which forms the basis for structural analysis and design. Numerous problems illustrate the text and somewhat complete it. Along with classical problems, they include cases of practical significance.
The author does not emphasize any particular procedure of solution, but instead considerable emphasis is placed on the solution of problems by the use of various methods. Most of the problems are worked out and those which are left as an exercise to the student are provided with answers or references to the original works.

About the author

Professor Vladimir Germanovich Rekach, D.Sc., is the Head of the Department of Strength of Materials at the Patrice Lumumba Peoples’ Friendship University in Moscow.

His main scientific interests are structural design, analysis of curved bars and vibration problems. The title of his doctoral thesis was “The Analysis of Spherical Shells”. He is the author of 28 articles and 3 books (3 as coauthor).

The book was translated from the Russian by M. Konyaeva and was published by Mir in 1979.

Many thanks to Akbar Azimi for the raw scans.

The Internet Archive Link

Note: There may be warping in some pages.



Chapter 1 Theory of Stress 9

I. Static and Dynamic Equilibrium Equations. 9
II. Surface Conditions. 12
III. State of Stress at a Point Problems. 13
III. Cylindrical Co-ordinates. 15
IV. Spherical Co-ordinates.
Problems. 15

Chapter 2 Theory of Strain 24

I. Strain Equations in Orthogonal Co-ordinates 24
II. State of Strain at a Point 28
III. Cesaro’s Formulas 29
Problems 30

Chapter 3 Basic Equations of the Theory of Elasticity and Their Solution or Special Cases 40

I. Orthogonal Curvilinear Co-ordinates 40
II. Rectangular Co-ordinates 41
III. Cylindrical Co-ordinates 43
IV. Spherical Co-ordinates 44
Problems 46

Chapter 4 General Solutions of the Basic Equations of the Theory of Elasti­city. Solution or Three-dimensional Problems 66

I. Harmonic Equation (Laplace’s ) 66
II. Biharmonic Equation 66
III. Boundary Value Problems for the Harmonic and Biharmonic Equations 72
IV. Various Forms of the General Solutions of Lame’s Equations 79
Problems 83

Chapter 5 Plane Problem in Rectangular Co-ordinates 106

I. Plane Stress 106
II. Plane Strain 108
III. Solutions of Basic Equations 109
Problems 119

Chapter 6 Plane Problem in Polar Co-ordinates. 151

I. Plane Stress 153
II. Plane Strain 153
III. Solution of Basic Equations 153
Problems 158

Chapter 7 Torsion of Prismatic and Cylindrical Bars 184

I. Pure Torsion of Bars of Constant Section 184
II. Pure Torsion of Circular Bars (Shafts) of Variable Section 187
Problems 194

Chapter 8 Thermal Problem 210

I. Steady-state Thermal Process 210
II. Transient Thermal Process 216
Problems 217

Chapter 9 Contact Problem. 236

I. The action of punches on an Elastic Half-plane 236
II. The Action of Punches on an Elastic Half-space 239
III. Contact Between Two Elastic Bodies 240
Problems 240

Chapter 10 Dynamic Problem. 267

I. Simple Harmonic Motion 267
II. Propagation of Volume Waves in an Elastic Isotropic Medium 269
III. Wave propagation over the surface of an elastic isotropic body 272
IV. Excitation of Elastic Waves by Body Forces 275
VI. Deformation of solids Under Centrifugal Forces 276
VI. Plane Dynamic Problems 277
VII. Thermodynamic Problem 281
Problems 283

References 302
Author Index 308
Subject Index 310

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Theoretical Electrochemistry – Antropov

In this post, we will see the book Theoretical Electrochemistry by L. I. Antropov.

Antropov - Theoretical Electrochemistry - Mir - 1972 copy

About the book (from the Preface)

In selecting the material and the order of presentation for this work I have been guided by the definition of electrochemistry, given by Kislyakovsky in 1912, as the science “concerned with the study of the phenomena accompanying the direct conversion of chemical energy into electrical and vice versa”. This definition was taken further by Pisarzhevsky, who was the first to formulate clearly the prerequisites for mutual conversion of chemical and electrical forms of energy and introduce the concept of electrochemical system in which this process is possible. Our presentation is based on the theory of electrochemical systems, their constituent parts and their possible states. It seems to me that these principles permit one to visualize electrochemistry as an integral whole and independent, self-contained discipline and clearly define the boundaries separatum it from closely related sciences.

Much attention is paid to disclosing the physical content of electrochemical phenomena and the essence of the related theoretical conceptions The mathematical apparatus is relatively simple, and only the general principles of electrochemical experiment are given. Experimental procedures are described in more detail only where it is necessary for the understanding of the nature of the process in question or the essence of the theoretical views concerned.

In writing this textbook I have tried to cover all the basic aspects of theoretical electrochemistry and to reflect as completely as possible the latest advances and trends in its development. I hope that this has been accomplished to some extent but though I have tried to be objective I have probably not avoided a certain preference what seemed to me more correct, and particularly more important and interesting. In this connection it would seem appropriate to recall Mendeleyev’s words in the preface to the fifth edition of his famous “Fundamentals of Chemistry”: – `in all objective expositions of science, there will always and inevitably be much that is subjective, bearing the stamp of the times and place… separate works, like a mirror, will reflect that which is near more clearly and strongly… although I have striven to make my book a true mirror—what is dear to me has involuntarily been reflected most sharply and illuminated more clearly, and presented, through the reflection, in all its pristine brightness’. The truth of these words has probably been felt by everyone who has tried to generalize the material of any science or branch of it.

The book was translated from the Russian by Artavaz Beknararov. And was published by Mir in 1972.

Many thanks to Akbar Azimi for original scans.

Some pages might have warping, but the book is readable.

The Internet Archive Link


Principal Symbols



Chapter 1. Theory of Electrolytic Dissociation 33

Chapter 2. Theory of Ionic Interaction 45

Chapter 3. Solvation and Hydration of Ions 69


Chapter 4. Electrical Conductance of Electrolytic Solutions 102

Chapter 5. Theoretical Interpretation of the Electrical Conductance of Electrolytes 123

Chapter 6. Diffusion in Electrolyte Solutions 142


Chapter 7. Equilibrium Electrode Potential 155

Chapter 8. Electrochemical Systems 190

Chapter 9. The Mechanism of Buildup of Electromotive Force and the Nature of Electrode Potentials 209


Chapter 10. Electrokinetic and Electrocapillary Phenomena 243

Chapter 11. The Structure of the Electric Double Layer at the Electrode-Electrolyte Interface 282


Chapter 12. The Chemical Effect of Electric Current 297

Chapter 13. The Kinetics of Electrode Processes 308

Chapter 14. Concentration Polarization 317

Chapter 15. Phase Overpotential 343

Chapter 16. Electrochemical Overpotential 360

Chapter 17 Some Methods of Investigating Electrode Kinetics 388

Chapter 18 Polarography 395


Chapter 19 The Hydrogen Evolution Reaction 411

Chapter 20 The Kinetics of the Oxygen Evolution Reaction 442

Chapter 21 The Kinetics of Electrochemical Reduction and Oxidation 452

Chapter 22 Electrodeposition of Metals from Solutions 477

Chapter 23 Electrochemical Dissolution and Passivity of Metals

Chapter 24 Electrochemical Corrosion of Metals 511

Chapter 25 Some Problems of Modern Electrochemistry 538

Bibliography 548

Name Index 551

Subject Index 555

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Mirtitles on Twitter

After some deliberation and discussion we have finally decided to be on Twitter. Some years back when this was suggested by one of the users. At that time we had decided against it. But for now, we will run this as an experiment for some time and see where it goes. So here we are:

Screenshot 2020-05-11 at 18.44.59

Updates will also be available via this channel in the future. We will use hashtag #mirtitles so keep a lookout for it.

Please do follow and spread the word.

Happy reading!

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Nonlinear Phenomena in Plasma Physics and Hydrodynamics – Sagdeev (Ed.)

In this post, we will see the book Nonlinear Phenomena in Plasma Physics and Hydrodynamics edited by R.Z.Sagdeev. This book is part of the Advances
in Science and Technology in the USSR Physics Series

Sagdeev (Ed.) - Nonlinear Phenomena in Plasma Physics and Hydrodynamics - Mir - 1986_0000

About the book (From the Preface)

The modern theory of nonlinear phenomena is going through a period of explosive growth. Each “invention” in the field is disseminated rapidly, generating general interest and unexpected applications. This was for instance the case with solitons, strange attractors, and stochasticity. That scientists from each of the different branches of the theory of nonlinear phenomena should cooperate needs no proof, and the value of this cooperation could be seen at a conference held in Kiev on nonlinear and turbulent processes in physics.* The same approach has been adopted for this collection, which includes articles on regular nonlinear phenomena (vortices, solitons, auto-waves) and some on stochasticity and turbulence. In addition, the collection includes two mathematical articles that develop the Kolmogorov-Amold-Moser theory, the importance of which for the theory of nonlinear dynamic systems is undoubted.

The articles are to some degree grouped around the nonlinear problems of plasma physics and hydrodynamics, in their broadest sense.

Hydrodynamics and plasma physics are traditional sources of exciting problems and ideas for the physics of nonlinear phenomena. We need only recall the classical examples of the discovery of solitons in shallow water, the exact integrability of the Korteweg-de Vries equation, and the discoveries of a strange attractor in the Lorcntz system and stochasticity in Hamiltonian systems with small numbers of degrees of freedom.

These ideas and results, all stimulated by problems in hydrodynamics and plasma physics, quickly gained more general significance for physics as a whole. In turn, many new and efficient techniques are tested on such traditionally difficult subjects as turbulence. For instance, there is the recent application to turbulence of the renormalization group methods, which were successfully employed first in field theory and the physics of phase transitions.

Finally, all this culminates in general fund of knowledge in the
physics of nonlinear phenomena. I hope that the publication of
this collection will advance the progress of physics.

The book was translated from the Russian by Valerii Ilyushchenko, and was first published by Mir in 1986.

Many thanks to Akbar Azimi for providing the raw 2-in-1 scans. We cleaned and OCRed the scans.

The Internet Archive Link

This book has an essay by A. Zhabotinsky of the Belousov–Zhabotinsky reaction


Preface 7

Vortices In Plasma and Hydrodynamics by A.B. Mikhailovskii

Introduction 8
Nonlinear Equations for Rossby Waves 12
The Simplest Nonlinear Equations for Drift Waves 14
Vector Vortical Structures 16
Scalar Vortical Structures 18
Further Development of Concepts Concerning Electrostatic Vortices in Plasma 19
Electromagnetic Vortices 22
Conclusion 24
References 28

Oscillations and Bifurcations in Reversible Systems by V. I. Arnol’d and M. B. Sevryuk 31

Introduction 31
Reversible Mappings 32
Reversible Flows 33
Integrable Reversible Mappings and Vector Fields 34
Kolmogorov’s Tori 35
Weak Reversibility 37
The Local Theory 37
Weak Reversibility in a Local Situation 42
Periodic Solutions 42
Kolmogorov’s Tori for Additional “Even” Coordinates 44
The Local Theory for Additional “Even” Coordinates 45
Application to Reversible Equations 48
Kon-Autonomour Reversible Systems 49
The Lyapunov-Devaney Theorem 51
The Resonance 1:1 52
Further Resonances l:N (N > 2) 54
References 83

Regular and Chaotic Dynamics of Particles In a Magnetic Field by R. Z. Sagdeev and C. U. Zaslavskii 85

Introduction 65
Equations of Motion 67
The Resonances of Longitudinal Motion 69
The Overlapping of the Resonances of Longitudinal Motion 72
A Kinetic Description 75
Equations of Transverse Motion 78
The Resonances of High-Energy Particles 83
Resonances in a Weak Magnetic Field 84
Generalization to a Wave Packet 85
A Kinetic Description of Transverse Motion 86
Quasi-Resonance Particles 88
References 92

The Renormalization Group Method and Kolmogorov-Arnold-Moser Theory by K. M. Khanin and Ya. G. Sinai 93

Introduction 93
Rectification of the Nonlinear Rotation of a Circle 97
Construction of Invariant KAM Curves by the Renormalization
Group Method 110
References 118

Nonlinear Problems of Turbulent Dynamo by Ya B, Zel’dovich and A. A. Rukmalkin 119

Introduction 119
Nonlinear Mean Field Dynamo 121
MHD Turbulence 130
References 135

Problems of the Theory of Strong Turbulence and Topological Solitons by R. Z. Sagdeev, S. S. Molseev, A. V. Tur, and V. V. Yanovskii 137

Introduction 137
The Scaling Group and Functional Method 140
“Null-Modes” and the Self-Similar Spectrum 152
Invariant Properties of Hydrodynamic Models and Topological Solitons 163
References 180

Self-Oscillations and Auto-Waves in Chemical Systems by A. M. Zhabotinskii 183

Introduction 183
Experimental Studies 184
Theoretical Studies 195
Conclusion 207
References 208

Auto-Waves In Biologically Active Media by V. I. Krinskii 210

Introduction 210
Mathematical Description 211
Local Sources of Auto-Waves 213
Cardiac Disorders 215
Mathematical Simulation of Auto-Wave Sources 216
A Chemically Active Medium 216
New Auto-Wave Modes 217
Wave Sources in Three-Dimensional Active Media 217
The Effect of Medium Parameters on Auto-Wave Sources 218
An Anomalous Reverberator 219
Theoretical Studies of Reverberators 220

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Elements Of The Applied Theory Of Elastic Vibration – Panovko

In this post, we will see the book Elements Of The Applied Theory Of Elastic Vibration by Ya. Panovko.

Panovko - Elements of the Applied Theory of Elastic Vibration - Mir - 1971_0000

About the book

We may distinguish at least the following live sufficiently inde­pendent categories of vibratory processes differing in their nature:

free vibrations, i.e., vibrations which are performed by a mecha­nical system having no energy supply from outside if the system is disturbed from its position of equilibrium and then released;

critical states of rotating shafts and rotors which consist in a sudden increase in the deflections of their axes at definite speeds of rotation (or in definite ranges of speeds);

forced vibrations which result when the mechanical system is acted on by fluctuating external forces (driving forces);

parametric vibrations caused by periodic variations of the para­ meters of a system (for example, its stiffness);

self-excited vibrations, i.e., vibratory processes which are main­tained by constant sources of energy of a non-vibratory nature.

Each of these categories of vibratory processes is discussed in the appropriate chapter.

The book was translated from the Russian by M. Konyaeva and was published by Mir in 1971.

Many thanks to Akbar Azimi for providing the raw scan 2-in-1 page scans. We cleaned the book with OCR.

The Internet Archive Link


Notation. 7

Introduction. 9


1. Number of Degrees of Freedom of an Elastic System. 11
2. Classification of Forces. 15
3. Methods for Setting Up Equations of Motion in the General Case. 22

CHAPTER II. Free vibrations . 24

4. Linear Systems of One Degree of Freedom Without Inelastic Resistances. 24
5. Effect of Inelastic Resisting Forces on Free Vibrations
of Linear Systems of One Degree of Freedom. 56
6. Undamped Systems of One Degree of Freedom with Non-Linear Restoring Forces. 68
7. Linear Systems of Several Degrees of Freedom. 87
8. Vibrations of Bars of Uniform Section (Exact Solution) 118
9. Vibrations of Ban of Variable Section. 138
10. Two-Dimensional Vibrations of Disks. 147
11. Flexural Vibrations of Disks. 153
12. Flexural Vibrations of Rectangular Plates. 157


13. Shaft with One Disk. 161
14. Effect of Friction. 174
15. Automatic Balancing of Rotating Shafts. 185
16. Critical States of Helicopter Rotors. 187
17. Shalt with Several Disks. Rigid Rotor on Elastic Supports 190


18. Linear Systems of One Degree of Freedom without Inelastic Resistances. 193
19. Linear Systems of One Degree of Freedom with Inelastic Resisting Forces. 226
20. Systems with Non-Linear Restoring Forces (Single Degree of Freedom). 241
21. Linear Systems of Several Degrees of Freedom. 249
22. Linear Systems with Distributed Parameters. 269


23. Basic Equation. 279
24. Cases of Periodic Variation of Stiffness. 283
25. Cases of Periodic Variation of Parametric Loads. 285
26. Pendulum with a Vibrating Point of Suspension. 288
27. Cases of Periodic Variation of the Inertia of a System. 289


28. Nature of Self-Excited Vibrations. 293
29. Self-Excited Vibrations of Quasi-Linear Systems. 298
30. Self-Excited Relaxation Vibrations. 304

Index. 314

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Algunos libros de matemática en Español (Some mathematics books in Spanish)

While browsing through The Internet Archive I stumbled across a few mathematics books in Spanish. We have some of these titles in English, but not all.

All credits to The Internet Archive user @librosmir


Curso De Algebra Superior A. Kurosch


Algebra Lineal V. Voevodin


Fundamentos Del Análisis Matemático 1 V. Ilín & E. Pozniak


Fundamentos Del Análisis Matemático 2 V. Ilín & E. Pozniak


Fundamentos Del Análisis Matemático 3 V. Ilín & E. Pozniak


Geometría Elemental A. Pogorélov


LPM ( 08) Resolución De Ecuaciones En Números Enteros A. Guelfond

MIR_LPM_Resolución_de_ecuaciones_en_números_enteros._A. O. Guelfond_0000

LPM Resolución De Ecuaciones En Números Enteros. A. O. Guelfond


Geometría Superior N. Efimov


Problemas De Geometría Analítica D. Kletenik


Problemas De Geometría Descriptiva V. Gordon, Y. Ivanov & T. Solntseva


Problemas De Geometría Diferencial A. Fedenko


Geometría Moderna B. Dubrovin, S. Nóvikov & A. Fomenko


Geometría Diferencial A. Pogorélov


Geometría N. Yákovliev


Curso Breve De Geometría Analítica N. Efimov


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Engineering Methods for Analysing Strength and Rigidity – Glushkov

In this post, we will see the book Engineering Methods for Analysing Strength and Rigidity by G. Glushkov.


About the book

The book is a theoretical treatise on the subject of higher order moments. The theory of moments developed into a specific branch of mathematics which became a useful tool for solving com­plicated problems in structural mechanics. A number of Soviet scientists developed the so-called moment-operational method, which has proved to be extremely efficient for solving various pro­blems of modern engineering. These problems arise when non-linear elasticity must be taken into account, when precise designing of non-uniform structural elements is required, when the loading of a structure is essentially non-uniform, etc.

The moment-operational method has been widely employed for compiling manuals containing numerous tables and formulas for designing beams, arches and frames. A number of scientific research works and textbooks present the theory of moments of higher order methods examples of problems solved by the moment-operational method.

The knowledge of the theory of higher moments as well as of the moment-operational method will serve to extend the field of their application to new problems.

The book was translated from the Russian by N. Lebedinsky and was published by Mir in 1974.

Many thanks to Akbar Azimi for providing the raw scans. We did the cleaning from 2-in-1 scans. There might be warping in some pages but the text overall is very readable.

The Internet Archive Link


Part 1 Moments of Higher Order: Theory and Application 9

Chapter 1. Theory of Moments 9

1. General Concept of Moments of Area 9
2. Moments as Geometric Characteristics of Beam Cross Sections 18
3. Uniaxial Moments of Point Forces and Couples 36
4. Uniaxial Moments of Balanced and Unbalanced Systems 40
5. Uniaxial Moments of Areas of Simple Figures 45
6. Uniaxial Moments of Areas of More Complicated Figures 52
7. Uniaxial Moments of Compound Loads 56
8. Moments of Higher Order and Generalized Forces 64

Chapter II. Application of Theory of Moments 73

9. Rigidity or Uniform Beams 73
10. Geometrical Interpretation of Moments 74
11. Calculation of Displacement Integrals in Rod Systems 83
12. Application of Higher Moments to Loading of Parabolic Influence Lines 92
13. Formulas for Statically Indeterminate Structures 94
14. Rigidity of Beams Composed of Prismatic Parts 140
15. Moments of Area of Flexibility Diagram for Non-Uniform Beams 145

Part II Moment-Operational Method: Theory and Application 160

Chapter III. Moment-Operational Method 160

16. Principles of Moment-Operational Method 160
17. Bimoments 162
18. Differential and Integral Bimoments 163
19. Application of Moment-Operational Method for Solving
Linear Differential Equations 170

Chapter IV. Rigidity of Non-Uniform Beams 173

20. Determination of Displacements by Coefficients of Flexibility Polynomial Expression 173
21. Determination of Displacements by Derivatives of Flexibility Analytical Expression 178
22. Determination of Displacements by Flexibility Integrals 182
23. Dermination of Displacements when Rigidity Follows Power 194
24. Determination of Displacement Integrals by Coefficients of Flexibility Polynomial 196
25. Determination of Displacement Integrals by Derivatives of Flexibility Analytical Expression 199

Chapter V. Multispan Non-Uniform Beams 202

28. Equation of Three Moments in Flexibility Polynomial Coeffi­cients 202
27. Equation of Three Moments in Derivatives of Analytically Expressed Flexibility 207
28. Equation of Three Moments in Flexibility Integrals 210
29. Mohrs Integrals for Non-Uniform Beams 219

Chapter VI. Beams on Elastic Foundation 223

30. General 223
31. Prismatic Beams on Foundation of Constant Rigidity 224
32. Prismatic Beams on Foundation of Linear Rigidity 227
33. Beams on Foundation of Hyperbolic Rigidity 229
34. Beams on Elastic Foundation with Moment Reaction 236

Chapter VII. Beams Under Combined Flexure and Compression 238

35. General 238
36. Prismatic Beams Under Arbitrary Transverse Loads and Constant Axial Forces 239
37. Rotating Rod of Constant Rigidity Under Compression and Flexure 255
38. Prismatic Beam Under Arbitrary Transverse Load and Uni­formly Distributed Axial Forces 260
39. Prismatic Beam Under Arbitrary Transverse Load and Linear Axial Forces 270
40. Prismatic Beam Under Arbitrary Transverse Load and Axial Law Distributed Along the Beam According to Polynomial 283

Chapter VIII. Application of Moment-Operational Method to Certain Complex Problems 285

41. Stability of Bars Under Axial Compression 285
42. Beams on Elastic Foundation Under Combined Compression and Bending 290
43. Non-Uniform Beam Under Axial Force 294
44. Higher Moments of Vector Quantities in Space 306
45. Rigidity of Beams: General Case of Non-Linear Stress-Strain Relationship 320

Chapter IX. Application of Moment-Operational Method to Structural Mechanics of Ships 331

46. Flexure of Irregular Decks 331
47. Non-Uniform Beams on Elastic Foundation 341
48. Stability and Vibration of Irregular Decks 346

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Questions and Answers in School Physics – Tarasov and Tarasova (LaTeX version)

In this post, we will see the book Questions and Answers in School Physics by Lev Tarasov and Aldina Tarasova. This post is for the LaTeX version of the book, earlier scanned book can be found here.
Tarasov-Tarasova-Questions-And-Answers-In-School-Physics-MirTitles-2020 copy

This book holds a special place for me, as this book helped me understand many subtle points in physics. Also, this was the first book that I have ever scanned and had added to gigapedia when it was extant. Also, this was one of the first books that I took to typeset in LaTeX, almost a decade back, but gave up after many attempts and the project was untouched for several years. At end of 2019 I restarted the work and here we are.

One major challenge remains to convert the 130 odd diagrams to purely LaTeX using TikZ. I have done this for some figures (~6-7), but most of them are from the scans. I will do it as and when time allows. And of course you are free to contribute as well. Any help in this regard would be highly appreciated.

I have done a round of copy-editing, but still minor typos may exist here and there, (hopefully there are no major typos or screw-ups). So do report if you find any. Earlier scan had two pages which were missing (pages 36-37), they have been added in the current version, so this version is complete. We have also re-scanned the full page figures of section heads and coloured them. Many thanks to psmitak for the scans!

About the typesetting
The typesetting was fun, and I am pleased with the results. A lot of help was derived from questions on

The main font used isURW-Garamond with mathdesign, while the sans font is TeX Gyre Adventor. The template used for the typesetting is tufte-book and the paper size is b5. The colour scheme used is Maroon and SteelBlue from svgnames of xcolor package of LaTeX along with DarkGray. I have, at times, highlighted questions using Maroon and answers or pedagogically significant remarks using SteelBlue. This is mostly done, if not completely done. Hope that this typeset version is helpful!

The Internet Archive Link

Gitlab Link for project files

PS: Next in line is Tarasov’s Basic Concepts of Quantum Mechanics – one round is done, final copy-editing is currently in progress. A few glimpses from that project:

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