## The Code of Life – Shvarts

In this post, we will see the book The Code of Life by A. Shvarts.
In this book the author relates in popular language about the latest attainments of biology and medicine, and about the future of these sciences.
The reader will learn about exciting operation on the heart, the mystery of cancer, the use of electronics in – medicine and about ingenious experiments aimed at extracting fresh information. He will get acquainted with viruses and the construction of the living cell, and will learn about the role of the new and rapidly developing molecular biology.
Anatoly Shvarts
Physician and writer Anatoly Shvarts had done much to popularize biology and medicine. He has written several widely-read books about Russian doctors and physiologists.
In “The Code of Life” Shvarts takes the present-day level of biology and medicine and extends it into the future.
The book was translated from the Russian by George Yankovsky and was published by Peace publishers in 1966.
CONTENTS
Part One Medicine takes off 8
HEALING THE HEART 9
In a Vicious Circle 10
Three Barriers 14
Cold—Enemy or Friend? 20
The “Sputnik” of Surgery 26
THE DOCTOR AND THE ELECTRON 29
Interviewing the Heart 31
Surgery in Full View 41
Diagnostic Complex 49
An Electronic Colleague 61
IRON HEALTH 67
The Iron Hand 68
Farsighted Skin 73
One Kidney in Reserve 79
The Formula of the Heart 83
FIGHTING OBSTREPEROUS TISSUE 90
The First Find 91
Strange Geography 95
Wandering Carcinogens 98
Magic Bullets 102
IN THE DEPTHS OF THE LIVING 106
Hours, Not Days! 107
The Seeds of Life 112
Hormone Plantations 117
The Heart of an Eagle 121
A Ray of Hope 126
Part TWO. THE TREASURE HOUSE OF THE CELL 136
NEVER GROWING OLD 137
The Anatomy of the Eiffel Tower 137
What People Live by 141
The Lymphocyte Builder 146
Prometheus and Monkeys 148
The Best Operation 150
VIRUS OF MANY GUISES 154
Ailment in Seven-League Boots 154
The Enemy Attacks 158
How the Virus was Tamed 162
Counterblow 164
A TRIP INTO THE MUSCLE 169
A Miracle of Molecular Technology 171
The Fire of Life 176
Pulsed Messengers   181
THE BATTLEFIELD OF IMMUNITY   185
Yours and Mine 185
The Tribulations of Insulin 189
The Profile of a Molecule 192
Medicine of the Future 198
THE CODE OF LIFE  202
Inside the Cell 203
Protein on the Production Line 207
Who? 217
Disowning One’s Own 225
NEWS FROM INSIDE THE CELL 228
A Substance or a Being? 230
This is How  234
A Tilt with the Invisible. 238
Problem “X” 247
Virus Hunters 261

## How reliable is the brain? -Asratyan, Simonov

In this post, we will see the book How reliable is the brain? by E. Asratyan and P. Simonov.

The book deals with topical problems of contempo­rary neurophysiology related to the restoration of impaired functions of the central nervous system.

The fundamental principles underlying the work of the brain, which enable it to function for many years without interruption, today command the interest of experts not only in medicine and biology, but in automa­tion as well. This is because these principles can be utilized to make computing systems more reliable.

The book was translated from the Russian by Boris Belitsky and was published by Mir in 1960s (exact date is not given).

CONTENTS
THE NO. 1 PROBLEM 7
THE CENTRAL “CONTROL PANEL’ OF THE ORGANISM 14
PROTECTIVE INHIBITION 58
LATENT RESERVES 109
INDEPENDENCE AND CENTRALISM 124
THE “SUPREME ORGAN’’ OF RESTORATION AND DEFENCE 140
LEARNING FROM NATURE 171

## Geometry – Pogorelov

In this post, we will see the book Geometry by A. Pogorelov.

This is a manual for the students of universities and teachers’ training colleges. Containing the compulsory course of geometry, its particular impact is on elementary topics. The book is, therefore, aimed at professional training of the school or university teacher-to-be. The first part, analytic geometry, is easy to assimilate, and actually reduced to acquiring skills in applying algebraic methods to elementary geometry.
The second part, differential geometry, contains the basics of the theory of curves and surfaces. The third part, foundations of geometry, is original. The fourth part is devoted to certain topics of elementary
geometry. The book as a whole must interest the reader in school or university teacher’s profession.

The book was translated from the Russian by Leonid Levant, Aleksandr Repyev and Oleg Efimov and published by Mir in 1987.

All credits to the original uploader. We have converted to pdf from djvu and added bookmarks/OCR to pdf. On a personal note, I am not a big fan of djvu format though it has a smaller size.

Contents

Preface 10

Part One. Analytic Geometry 11

Chapter I. Rectangular Cartesian Coordinates in the Plane 11

1. Introducing Coordinates in the Plane 11
2. Distance Between Two Points 12
3. Dividing a Line Segment in a Given Ratio 13
4. Equation of a Curve. Equation of a Circle 15
5. Parametric Equations of a Curve 17
6. Points of Intersection of Curves 19
7. Relative Position of Two Circles 20
Exercises to Chapter I 21

Chapter II. Vectors in the Plane 26

1. Translation 26
2. Modulus and the Direction of a Vector 28
3. Components of a Vector 30
5. Multiplication of a Vector by a Number 31
6. Collinear Vectors 32
7. Resolution of a Vector into Two Non-Collinear Vectors 33
8. Scalar Product 34
Exercises to Chapter II 36

Chapter III. Straight Line in the Plane 38

1. Equation of a Straight Line. General Form 38
2. Position of a Straight Line Relative to a Coordinate System 40
3. Parallelism and Perpendicularity Condition for Straight Lines 41
4. Equation of a Pencil of Straight Lines 42
5. Normal Form of the Equation of a Straight Line 43
6. Transformation of Coordinates 44
7. Motions in the Plane 47
8. Inversion 47
Exercises to Chapter III

Chapter IV. Conic Sections 53

1. Polar Coordinates 53
2. Conic Sections 54
3. Equations of Conic Sections in Polar Coordinates 56
4. Canonical Equations of Conic Sections in Rectangular Cartesian Coordinates 57
5. Types of Conic Sections 59
6. Tangent Line to a Conic Section 62
7. Focal Properties of Conic Sections 65
8. Diameters of a Conic Section 67
9. Curves of the Second Degree 69
Exercises to Chapter IV 71

Chapter V. Rectangular Cartesian Coordinates and Vectors in Space 76

1. Cartesian Coordinates in Space. Introduction 76
2. Translation in Space 78
3. Vectors in Space 79
4. Decomposition of a Vector into Three Non-coplanar Vectors 80
5. Vector Product of Vectors 81
6. Scalar Triple Product of Vectors 83
7. Affine Cartesian Coordinates, 84
8. Transformation of Coordinates 85
9. Equations of a Surface and a Curve in Space 87

Exercises to Chapter V 89

Chapter VI.

Plane and a Straight Line in Space 95

1. Equation of a Plane 95
2. Position of a Plane Relative to a Coordinate System 96
3. Normal Form of Equations of the Plane 97
4. Parallelism and Perpendicularity of Planes 98
5. Equations of a Straight Line 99
6. Relative Position of a Straight Line and a Plane, of Two Straight Lines 100
7. Basic Problems en Straight Lines and Planes 102
Exercises to Chapter VI 103

1. Special System of Coordinates 109
2. Classification of Quadric Surfaces 112
3. Ellipsoid 113
4. Hyperboloids 115
5. Paraboloids 116
6. Cone and Cylinders 118
7. Rectilinear Generators on Quadric Surfaces 119
8. Diameters and Diametral Planes of a Quadric Surface 120
9. Axes of Symmetry for a Curve. Planes of Symmetry for a Surface 122
Exercises to Chapter VII 123

Part Two. Differential Geometry 126

Chapter VIII. Tangent and Osculating Planes of Curve 126

1. Concept of Curve 126
2. Regular Curve 127
3. Singular Points of a Curve 128
4. Vector Function of Scalar Argument 129
5. Tangent to a Curve 131
6. Equations of Tangents for Various Methods of Specifying a Curve 132
7. Osculating Plane of a Curve 134
8. Envelope of a Family of Plane Curves 136
Exercises to Chapter VIII 137

Chapter IX. Curvature and Torsion of Curve 140

1. Length of a Curve 140
2. Natural Parametrization of a Curve 142
3. Curvature 142
4. Torsion of a Curve 145
5. Frenet Formulas 147
6. Evolute and Evolvent of a Plane Curve 14

Exercises to Chapter IX 149

Chapter X. Tangent Plane and Osculating Paraboloid of Surface 151

1. Concept of Surface 151
2. Regular Surfaces 152
3. Tangent Plane to a Surface 153
4. Equation of a Tangent Plane 155
5. Osculating Paraboloid of a Surface 156
6. Classification of Surface Points 158
Exercises to Chapter X 159

Chapter XI. Surface Curvature 161

1. Surface Linear Element 161
2. Area of a Surface 162
3. Normal Curvature of a Surface 164
4. Indicatrix of the Normal Curvature 165
5. Conjugate Coordinate Lines on a Surface 167
6. Lines of Curvature 168
7. Mean and Gaussian Curvature of a Surface 170
8. Example of a Surface of Constant Negative Gaussian Curvature 172
Exercises to Chapter XI 173

Chapter XII. Intrinsic Geometry of Surface 175

1. Gaussian Curvature as an Object of the Intrinsic Geometry of Surfaces 175
2. Geodesic Lines on a Surface 178
3. Extremal Property of Geodesics 179
4. Surfaces of Constant Gaussian Curvature 180
5. Gauss-Bonnet Theorem 181
6. Closed Surfaces 182
Exercises to Chapter XII 184

Part Three. Foundations of Geometry 186

Chapter XIII. Historical Survey 186

1. Euclid’s Elements 186
2. Attempts to Prove the Fifth Postulate 188
3. Discovery of Non-Euclidean Geometry 189
4. Works on the Foundations of Geometry in the Second Half of the 19th century 191
5. System of Axioms for Euclidean Geometry according to D. Hilbert 192

Chapter XIV. System of Axioms for Euclidean Geometry and Their Immediate Corollaries 194

1. Basic Concepts 194
2. Axioms of Incidence 195
3. Axioms of Order 196
4. Axioms of Measure for Line Segments and Angles 197 5. Axiom of Existence of a Triangle Congruent to a Given One 199
6. Axiom of Existence of a Line Segment of Given Length 200
7. Parallel Axiom 202
8. Axioms for Space 202

Chapter XV. Investigation of Euclidean Geometry Axioms 203

1. Preliminaries 203
2. Cartesian Model of Euclidean Geometry 204
3. “Betweenness” Relation for Points in a Straight Line. Verification of the Axioms of Order 205
4. Length of a Segment. Verification of the Axiom of Measure for Line Segments 207
5. Measure of Angles in Degrees. Verification of Axiom III* 208
6. Validity of the Other Axioms in the Cartesian Model 210
7. Consistency and Completeness of the Euclidean Geometry Axiom System 212
8. Independence of the Axiom of Existence of a Line Segment of Given Length 214
9. Independence of the Parallel Axiom 216
10. Lobachevskian Geometry 218
Chapter XVI. Projective Geometry 222

1. Axioms of Incidence for Projective Geometry 222
2. Desargues Theorem 223
3. Completion of Euclidean Space with the Elements at Infinity 225
4. Topological Structure of a Projective Straight Line and Plane 226
5. Projective Coordinates and Projective Transformations 228
6. Cross Ratio 230
7. Harmonic Separation of Pairs of Points 232
8. Curves of the Second Degree and Quadric Surfaces 233
9. Steiner Theorem 235
10. Pascal Theorem 236
11. Pole and Polar 238
12. Polar Reciprocation. Brianchon Theorem 240
13. Duality Principle 241
14. Various Geometries in Projective Outlook 243
Exercises to Chapter XVI 245
Part Four. Certain Problems of Elementary Geometry 247

Chapter XVII. Methods for Solution of Construction Problems 247

1. Preliminaries 247
2. Locus Method 248
3. Similarity Method 250
4. Reflection Method 251
5. Translation Method 251
6. Rotation Method 252
7. Inversion Method 253
8. On Solvability of Construction Problems 255
Exercises to Chapter XVII 256

Chapter XVIII. Measuring Lengths, Areas and Volumes 258

1. Measuring Line Segments 258
2. Length of a Circumference 260
3. Areas of Figures 261
4. Volumes of Solids 265
5. Area of a Surface 267

Chapter XIX. Elements of Projection Drawing 268

1. Representation of a Point on an Epure 268
2. Problems Leading to a Straight Line 269
3. Determination of the Length of a Line Segment 270
4. Problems Leading to a Straight Line and a Plane 271
5. Representation of a Prism and a Pyramid 273
6. Representation of a Cylinder, a Cone and a Sphere 274
7. Construction of Sections 275
Exercises to Chapter XIX 277

Chapter XX. Polyhedral Angles and Polyhedra 278

1. Cosine Law for a Trihedral Angle 278
2. Trihedral Angle Conjugate to a Given One 279
3. Sine Law for a Trihedral Angle 280
4. Relation Between the Face Angles of a Polyhedra Angles 281
5. Area of a Spherical Polygon 282
6. Convex Polyhedra. Concept of Convex Body 283
7. Euler Theorem for Convex Polyhedra 284
8. Cauchy Theorem 285
9. Regular Polyhedra 288
Exercises to Chapter XX 289

Answers to Exercises, Hints and Solutions 291

## नन्हें मुन्नो के लिए भौतिकी – सिकारुक (Physics for Kids – Sikoruk)

In this post, we will see the book नन्हें मुन्नो के लिए भौतिकी – सिकारुक in Hindi (Physics for Kids – Sikoruk).

इस पुस्तक के बारें में

इस पुस्तक में  लेखक ने सरस ढंग से नन्हें-मुन्नो का भौतिकी की मुख्य परिघटनाओ व नियमों से परिचय कराया है। स्कूल में पढ़ाई शुरू करने से पूर्व भौतिकी की विभिन्न धारणाओं को अच्छी तरह समझने के लिए ये पुस्तक बच्चों को केवल पढ़कर सुनना ही पर्याप्त नहीं है।इसके लिए इसमें वर्णित परिघटनाओं का बड़ों के साथ बैठकर प्रयोग तथा प्रेक्शन करना सर्वाधिक महत्वपूर्ण है। आशा है की रंगबिरंगी तस्वीरें पुस्तक को भली-भाँति समझने में काफ़ी सहायक सिद्ध होगी।

पुस्तक बच्चों और माता-पिता के एक साथ बैठकर पड़ने के उद्देश्य से लिखी गयी है।

In this book author has introduced main phenomenon and laws of physics to children in a simple way. Before starting the learning at school it is not sufficient to just read out this book to children for understanding various concepts in physics. For this, it is important the phenomena described in this book should be experimented and observed. We hope that the colourful pictures in the book will help in the understanding of the book.

This book has been written with the purpose of parents and children reading it together.

The sections cover major concepts in physics like sound, light, heat, speed, time, electricity and magnetism. The book is profusely illustrated with photographs of actual physical setups using dolls and other play materials.

The book was translated to Hindi from Russian by Ramindra Pal Singh and was published by Mir in 1987.

All credits to Guptaji

विषय सूची | Contents

ध्वनि | Sound

खिलौना वाइयलिन कैसे बना सकता है?

मचिस का टेलेफ़ोन

ध्वनि  कैसे तेज़ की जा सकती है?

ख़रगोश के कान लम्बे क्यूँ होते है?

अपनी आवाज़ कैसे देखी जा सकती है?

रिकार्ड से आवाज़  क्यों निकलती है?

प्रतिध्वनि

प्रश्न और प्रयोग | Questions and Experiments

प्रकाश | Light

सूरज की किरणों को एक जगह से दूसरी जगह कैसे पहुंचाया जा सकता है

दर्पण ओ का जादू

धूप में आमलेट कैसे बना सकते हैं

पुराने जमाने का कैमरा

प्रश्न और प्रयोग | Questions and Experiments

ऊष्मा | Heat

क्या हुआ कुछ गर्म होता है

बोतल से थर्मामीटर कैसे बनाया जा सकता है

माचिस के बिना आग कैसे जलाए जा सकती है

प्रश्न और प्रयोग | Questions and Experiments

द्रव गैस तथा ठोस पदार्थ | Solids, Liquids and Gases

बलून क्यों उड़ता है

हवा क्यों चलती है

द्रव पत्थर

बर्फ के खिलौने

बारिश क्यों होती है

प्रश्न और प्रयोग | Questions and Experiments

दिक् और गति | Time and Speed

तस्वीर के सैनिक से परेड कैसे कराई जा सकती है

कौन किधर जा रहा है

धूप की घड़ी

प्रश्न और प्रयोग | Questions and Experiments

जड़त्व  व जेट गति | Inertia and Jet Speed

आलसी  पहिए

मोहन जादूगर कैसे बन गया

जेट  डिब्बा

जेट खिलौने

खिलौना जिसने अंतरिक्ष पर विजय प्राप्त की

जहाज को पाल की क्या आवश्यकता है

पुरानी चक्की

पतंग  क्यों उड़ती है?

प्रश्न और प्रयोग | Questions and Experiments

विद्युत तथा चुंबकत्व | Electricity and Magnetism

थोड़ी सी विद्युत कैसे पैदा की जा सकती है?

बिजली के बल्बों की माला

चुंबाकों के बारे में

जादू की कील

प्रश्न और प्रयोग | Questions and Experiments

Posted in books, mir books, mir publishers, physics, science | | 7 Comments

## Fundamentals of Machine Design – Orlov

In this post, we will see the three out of five-volume set Fundamentals of Machine Design by P. Orlov.

The purpose of the present book is to offer the reader an attempt at a systematic exposition of rules for rational designing.

With all the diversity of the modern, machine-building the tasks facing the designer are similar in many respects. It is the reduction of the weight and specific metalwork weight of the machine, the improved suitability for industrial production, greater durability and reliability that are of importance for the design of any machine, the difference lying only in the relative significance of these factors. All this enables one to formulate the principles of rational designing as a code of general rules for machine building.

The prime intention of the book is to make the designer learn to work creatively. To design imaginatively means: to abstain from blindly copying the existing prototypes and to design meaningfully, selecting from the entire store of the design solutions offered by the present-day mechanical engineering the ones that are most suitable under given conditions; to be able to combine various solutions and find new, better ones, i. e., display initiative and put vim in the work; to continually improve the machines’ characteristics and to contribute to the progress in the given branch of mechanical engineering; to follow the dynamic development of the industry and devise versatile machines of long life, amenable to further modernization and capable of meeting the ever-growing demands of the national economy without running the risks of obsolescence for a long time to come.

Particular attention in the book is attached to the problems of durability and reliability. The author endeavoured to strongly emphasis the leading role of the designer in tackling these problems. In presenting the material the author followed the principle  “qui vidit—bis legit” (the one who sees reads twice). Most of the designers are individuals of visual thinking and visual memory.  For them a drawing or even a simple sketch means much more than many pages of explanatory notes. For this reason, each point in the text is accompanied by design examples.

To better the understanding most of the illustrations are arranged in such a way as to enable it to compare wrong and correct, inexpedient and expedient design versions.

The solutions given as correct are not the only possible ones. They should be regarded not as precepts, suitable for use in all cases, but rather as examples. In particular conditions other versions may prove more advisable.

All credits to the original uploader. Credits to edgato for posting the IA links.

Volume 1 Translated from the Russian by YU. TRAYNICHEV, published in 1976

Volume 2 Translated from the Russian by YU. TRAYNICHEV, published in 1976

Volume 3 Translated from the Russian by A. TROTSKY, published in 1977

Volume 4 (Not available, published 1977)

Volume 5 (Not available, published 1980)

## Operational Methods – Maslov

In this post, we will see the book Operational Methods by V. P. Maslov.

…This book is devoted to one, but sufficiently general operational method, which absorbs many operational methods known to date and allows for the uniform solution of both classical problems, involving differential equations with partial derivatives, and the absolutely new problems of mathematical physics, including those connected with non-linear equations in partial derivatives.

…This book on operational methods should be accessible to senior course students of mathematics and physics faculties at universities and departments of applied mathematics. This means that only a knowledge of classical analysis is required of the reader. The book provides explanations in sufficient volume of such concepts as the theory of Banach algebras of distributions (Chapter I), the theory of linear differential and difference equations (Sees. 1, 2, and 3 of Introduction), the theory of non-linear equations of the first order with partial derivatives (Chapter IV). This material may be also of use to the reader who is already familiar with these questions, because rather often it is not presented in traditional style, and adapted for further reference. The reader who studies the book thoroughly will be equipped to carry on independent research in the modern theory of linear, non-linear differential and differential-difference equations with partial derivatives.

…This book has been written in such a way as to serve the widest possible circle of readers. It is suitable for two methods of study. The reader, who seeks to avoid fine assessments and passing to the limit and only wishes to master the practical techniques for obtaining asymptotic solutions, may omit that part of the book which is devoted to functional analysis.

…The most effective way of mastering the subject, however, consists rather in first reading Introduction and then reading all the book in succession. The reader should nevertheless be warned that all these methods are not at all easy, because the book provides a new operational calculus-the calculus of ordered operators.

The book was translated from the Russian by V. Golo, N. Kulman and G. Voropaeva and was published by Mir in 1976.

Credits to the original uploader for the scan, in this link we have converted to pdf from djvu, added bookmarks and cover.

CONTENTS
Preface 7
Introduction to Operational Calculus 13
Sec. 1. Solution of Ordinary Differential Equations by the Heaviside Operational Method 13
Sec. 2. Difference Equations 20
Sec. 3. Solution of Systems of Differential Equations by the Heaviside Operational Method 22
Sec. 4. Algebra of Convergent Power Series of Noncommutative Operators 24
Sec. 5. Spectrum of a Pair of Ordered Operators 35
Sec. 6. Algebras with \mu-Structures 40
Sec. 7. An Example of a Solution of a Differential Equation 56
Sec. 8. Passage of the Equation of Oscillations of a Crystal Lattice into a Wave Equation 58
Sec. 9. The Concept of a Quasi-Inverse Operator and Formulation of
the Main Theorem 100

Chapter I Functions of a Regular Operator 147

Sec. 1. Certain Spaces of Continuous Functions and Related Spaces 149
Sec. 2. Embedding Theorems 154
Sec. 3. The Algebra of Functions of a Generator 158
Sec. 4. The Extension of the Class of Possible Symbols 173
Sec. 5. Homomorphism of Asymptotic Formulas. The Method of Stationary Phase 181
Sec. 6. The Spectrum of a Generator 188
Sec. 7. Regular Operators 194
Sec. 8. The Generalized Eigenfunctions and Associated Functions 198
Sec. 9. Self-Adjoint Operators as Transformers in the Schmidt Space 205

Chapter II Calculus of Noncommutative Operators 210
Sec. 1. Preliminary Definitions 210
Sec. 2. The Functions of Two Noncommutative Self-Adjoint Operators 224
Sec. 3. The Functions of Noncommutative Operators 228
Sec. 4. The Spectrum of a Vector-Operator 231
Sec. 5. Theorem on Homomorphism 239
Sec. 6. Problems 242
Sec. 7. Differentiation of the Functions of an Operator Depending on a Parameter 251
Sec. 8. Formulas of Commutation 256
Sec. 9. Growing Symbols 261
Sec. 10. The Factor-Spectrum 265
Sec. 11. The Functions of Components of a Lie Nilpotent Algebra and Their Representations 266

Chapter III Asymptotic Methods 273

Sec. 1. Canonical Transformations of Pseudodifferential Operators 273
Sec. 2. The Homomorphism of Asymptotic Formulas 294
Sec. 3. The Geometrical Interpretation of the Method of Stationary
Phase 301
Sec. 4. The Canonical Operator on an Unclosed Curve 303
Sec. 5. The Method of Stationary Phase 312
Sec. 6. The Canonical Operator on the Unclosed Curve Depending on Parameters Defined Correct to 0 ( 1/\omega ) 315
Sec. 7. V-Objects on the Curve 321
Sec. 8. The Canonical Operator on the Family of Unclosed Curves 327
Sec. 9. The Canonical Operator on the Family of Closed Curves 333
Sec. 10. An Example of Commutation of a Canonical Operator with a Hamiltonian 339
Sec. 11. Commutation of a Hamiltonian with a Canonical Operator 346
Sec. 12. The General Canonical Transformation of the Pseudodifferential Operator 348

Chapter IV Generalized Hamilton-Jacobi Equations 355

Sec. 1. Hamilton-Jacobi Equations with Dissipation 356
Sec. 2. The Lagrangean Manifold with a Complex Germ 360
Sec. 3. y-Atlases and the Dissipativity Inequality 372
Sec. 4. Solution of the Hamilton-Jacobi Equation with Dissipation 378
Sec. 5. Preservation of the Dissipativity Inequality. Bypassing Focuses Operation 386
Sec. 6. Solution of Transfer Equation with Dissipation 401

Chapter V Canonical Operator on a Lagrangean Manifold with a Complex Germ and Proof of the Main Theorem 419

Sec. 1. Quantum Bypassing Focuses Operation 419
Sec. 2. Commutation Formulas for a Complex Exponential and a Hamiltonian 440
Sec. 3. C-Lagrangean Manifolds and the Index of a Complex Germ 452
Sec. 4. Canonical Operator 469
Sec. 5. Proof of the Main Theorem 482
Appendix to Sec. 5 493
Sec. 6. Cauchy Problem for Systems with Complex Characteristics 503
Sec. 7. Quasi-Inverse of Operators with Matrix Symbols 519
Appendix. Spectral Expansion of T-products 545
Index 557

## Strength of Materials – Belyaev

In this post, we will see the book Strength of Materials by N. M. Belyaev.

The new edition of Strength of Materials by N. M. Belyaev has been published after 11 years. In 33 years that lapsed between the publication by N. M. Belyaev of the first edition in 1932 and the last fourteenth edition in 1965 a total of 675 000 copies of the book were sold, testifying to its wide popularity. During this period the book was periodically enlarged and revised by N. M. Belyaev and, after his death in 1944, by a group of four of his co-workers. This group, which prepared from the fifth to the fourteenth editions for publication, did not consider it proper to make substantial changes in the original work of N. M. Belyaev. Additions were done at one time or another only when they became absolutely necessary due to changes in standards and technical specifications and in the light of recent research.

In the present edition, prepared by the same group, a number of topics have been dropped either owing to their irrelevance to strength of materials or because they are rarely taught in the main course.

Considering the availability of a large number of problem books (see, for instance, Problems on Strength of Materials edited by V. K. Kachurin) on the market, most of the examples have been dropped from the present edition. Only examples that are essential for the explanation of theoretical part have been retained. For greater compactness the problem of design for safe loads has now been included in Chapter 26 For the first time the chapter includes the principles of design for limiting states, which though beyond the limits of the basic course of strength of materials are important enough to require an exposition of the basic concepts even at this stage of teaching.

The problems of strength, which in the previous editions occupied two chapters, have been grouped into one. The part dealing with actual stresses has been transferred to Chapter 2, where it has been presented in a sufficiently detailed manner. The tables containing data on materials have been dropped from the appendices. A part of the data on materials has been transferred to 8 Preface to the Fifteenth Russian Edition corresponding sections. The obsolete steel proliles grading has been replaced by new ones.

As in the previous editions it was our endeavour to preserve Belyaev’s style and method of presentation of material. Therefore the author’s text has in general been preserved. If Nikolai Mikhailovich Belyaev were alive today he would possibly write many things in a different way. However, since the book won wide popularity as written by N. M. Belyaev, we tried to preserve the original text as far as possible.

(perhaps someone with an engineering background can post a much better review)

The book was translated from the Russian by N. K. Mehta and was published by Mir in 1979. This is the fifteenth edition of the book.

All credits to the original uploader. Credits to Tor, db.jan for posting the links.

The Internet Archive Link (djvu only) from IA user quailhacker

The Internet Archive Link (pdf+other formats)

Contents

PART 1. Introduction. Tension and Compression

Chapter 1. Introduction 17

§ 1. The science of strength of materials 17
§ 2. Classification of forces acting on elements of structures 18
§ 3. Deformations and stresses 21
§ 4. Scheme of a solution of the fundamental problem of strength of materials 23
§ 5. Types of deformations 27

Chapter 2. Stress and Strain in Tension and Compression Within the Elastic Limit Selection of Cross-sectional Area 27

§ 6. Determining the stresses in planes perpendicular io tile axis of the bar 27
§ 7. Permissible stresses. Selecting the cross-sectional area 30
§ 8. Deformations under tension and compression. Hooke’s law 32
§ 9. Lateral deformation coefficient. Poisson’s ratio 36

Chapter 3. Experimental Study of Tension and Compression In Various Materials and
the Basis of Selecting the Permissible Stresses 40

§ 10. Tension test diagram. Mechanical properties of materials 40
§ 11. Stress-strain diagram 47
§ 12. True stress-strain diagram 48
§ 13. Stress-strain diagram for ductile and brittle materials 62
§ 14. Rupture in compression of brittle and ductile materials. Compression test diagram 64
§ 16. Comparative study of the mechanical properties of ductile and brittle materials 57
§ 16. Considerations in selection of safety factor 59
§ 17. Permissible stresses under tension and compression for various materials 64

PART II. Complicated Cases of Tension and Compression

Chapter 4. Design of Statically Indeterminate Systems for Permissible Stresses 66

$18. Statically indeterminate systems 66 § 19. The effect of manufacturing inaccuracies on the forces acting in the elements of statically indeterminate structures 73 § 20. Tension and compression in bars made of heterogeneous materials 77 § 21. Stresses due to temperature change 79 § 22. Simultaneous account for various factors 82 § 23. More complicated cases of statically indeterminate structures 85 Chapter 5. Account for Dead Weight In Tension and Compression* Design of Flexible Strings 88 § 24. Selecting the cross-sectional area with the account for the dead weight (in tension and compression) 86 § 25. Deformations due to dead weight 81 § 26. Flexible cables 92 Chapter 6. Compound Stressed State. Stress and Strain 99 § 27. Stresses along Inclined sections under axial tension or compression (uniaxial stress) 99 § 28. Concept of principal stresses. Types of stresses of materials 101 § 29. Examples oil biaxial and triaxial stresses. Design of a cylindrical reservoir 103 § 30. Stresses In a biaxial stressed state 107 § 31. Graphic determination of stresses (Mohr’s circle) 110 § 32. Determination of the. principal stresses with the help of the stress circle 114 § 33. Stresses in triaxial stressed state 117 § 34. Deformations In the compound stress 121 § 35. Potential energy of elastic deformation in compound stress 124 § 36. Pure shear. Stresses and strains. Hooke’s law. Potential energy 127 Chapter 7. Strength of Materials in Compound Stress 132 § 37. Resistance to failure. Rupture and shear 132 § 38. Strength theories 136 § 39. Theories of brittle failure (theories of rupture) 138 § 40. Theories of ductile failure (theories of shear) 140 § 41. Reduced stresses according to different strength theories 147 § 42. Permissible stresses in pure shear 149 PART III. Shear and Torsion Chapter 8. Practical Methods of Design on Shear 151 §43. Design of riveted and bolted joints 151 §44. Design of welded joints 158 Chapter 9. Torsion. Strength and Rigidity of Twisted Bars 164 § 45. Torque 164 § 46. Calculation of torques transmitted to the shaft 167 § 47. Determining stresses in a round shaft under torsion 168 § 48. Determination of polar moments of inertia and section moduli of a shaft section 174 § 49. Strength condition in torsion 176 § 50. Deformations in torsion. Rigidity condition 176 § 51. Stresses under torsion in a section inclined to the shaft axis 178 § 52. Potential energy of torsion 180 § 53. Stress and strain In dose-coiled helical springs 181 § 54. Torsion in rods of non-circular section 187 PART IV. Bending. Strength of Beams Chapter 10. Internal Forces In Bending. Shearing-force and Bending-moment Diagrams 198$ 55. Fundamental concepts of deformation in bending. Construction of beam supports 195
§ 56. Nature of stresses in a beam. Bending moment and shealine force 200
§ 57. Differential relation between the intensity of a continuous load, shearing force and bending moment 205
§ 58. Plotting bending-moment and shearing-force diagrams 207
§ 59. Plotting bending-moment and shearing-force diagrams for more complicated loads 214
§ 60. The check of proper plotting of Qr and M-diagrams 221
§ 61. Application of the principle of superposition of forces In plotting shearing-force and bending-moment diagrams 223

Chapter 11. Determination of Normal Stresses in Bending and Strength of Beams 225

§ 62. Experimental investigation of the working of materials in pure bending 225
§ 63. Determination of norma) stresses In bending. Hooke’s law and potential energy of bending 228
§ 64. Application of the results derived above in checking the strength of beams 235

Chapter 12. Determination of Moments of Inertia of Plane Figures 239

§ 65. Determination of moments of inertia and section moduli for simple sections 239
§ 66. General method of calculating the moments of inertia of complex sections 244
§ 67. Relation between moments of inertia about two parallel axes one of which is the central axis 246
§ 68. Relation between the moments of inertia under rotation of axes 247
§ 69. Principal axes of inertia and principal moments of inertia 250
§ 70. The maximum and minimum values oi the central moments of
inertia 254
§ 71. Application of the formula for determining normal stresses to
beams of non-symmetrical sections 254
§ 72. Radii of inertia. Concept of the momenta! ellipse 256
§ 73. Strength check, choice of section and determination of permissible load in bending 258

Chapter 13. Shearing and Principal Stresses In Beams 263

§ 74. Shearing stresses in a beam of rectangular section 263
§ 75. Shearing stresses in I-beams 270
§ 76. Shearing stresses in beams of circular and ring sections 272
§ 77. Strength check for principal stresses 275
§ 78. Directions the principal stresses 280

Chapter 14. Shear Centre. Composite Beams 283

§ 79. Shearing stresses parallel to the neutral axis. Concept of shear centre 233
§ 80, Riveted and welded beams 289

PART V. Deformation of Beams due to Bending

Chapter 15. Analytical Method of Determining Deformations 292

§ 81. Deflection and rotation oi beam sections 292
$82. Differential equation of the deflected axis 294 § 83. Integration oi the differentia) equation of the deflected axis of a beam fixed at one end 296 84. Integrating the differential equation of the deflected axis of a simply supported beam 299 § 85. Method of equating the constants of integration oi differential equations when the beam has a number of differently loaded portions 301 § 86. Method of initial parameters for determining displacements in beams 304 § 87, Simply supported beam unsymmetrically loaded by a force 305 § 88. Integrating the differential equation for a hinged beam 307 § 89. Superposition of forces 310 § 90. Differential relations in bending 312 Chapter 16. Graph-analytic Method of Calculating Displacement in Bending 313 § 91. Graph-analytic method 313 § 92. Examples of determining deformations by the graph-analytic method 317 § 93. The graph-analytic method applied to curvilinear bending-moment diagrams 320 Chapter 17. Non-uniform Beams 324 § 94. Selecting the section in beams of uniform strength 324 § 95. Practical examples of beams of uniform strength 325 § 96. Displacements in non-uniform beams 326 PART VI. Potential Energy. Statically Indeterminate Beams Chapter 18. Application of the Concept of Potential Energy in Determining Displacements 331 § 97. Statement of the problem 331 § 98. Potential energy in the simplest cases of loading 333 § 99. Potential energy ior the case of several forces 334 § 100. Calculating bending energy using internal forces 336 § 101. Castigliano’s theorem 337$ 102. Examples of application of Castigiiano’s theorem 341
$103. Method of introducing an external force 344 § 104. Theorem of reciprocity of works 346 § 105. The theorem of Maxwell and Mohr 347 § 106. Vereshchagin’s method 349 § 107. Displacements In frames 351 § 108. Deflection of beams due to shearing force 353 Chapter 19. Statically indeterminate Beams 356 § 109. Fundamental concepts 356 § 110. Removing static indeterminacy via the differential equation of the deflected beam axis 357 § 111. Concepts of redundant unknown and base beam 359 § 112. Method of comparison of displacements 360 § 113. Application of the theorems of Castigliano and Mohr and Vereshchagin’s method 362 § 114. solution of a simple statically Indeterminate frame 364 § 115. Analysis of continuous beams 366 § 116. The theorem of three moments 366 § 117. An example on application erf the theorem of three moments 372 § 118. Continuous beams with cantilevers. Beams with rigidly fixed ends 375 PART VII. Resistance Under Compound Loading Chapter 20. Unsymmetric Bending 378 § 119. Fundamental concepts 378 § 120. Unsymmetric bending. Determination of stresses 379 § 121. Determining displacements in unsymmetric bending 365 Chapter 21. Combined Bending and Tension or Compression 389 § 122. Deflection of a beam subjected to axial and lateral forces 389 § 123. Eccentric tension or compression 392 § 124. Core of section 396 Chapter 22. Combined bending and torsion 401 § 125. Determination erf twisting and bending moments 401 § 126. Determination of stresses and strength check In combined bending and torsion 404 Chapter 23. General Compound Loading 408 § 127. Stresses in a bar section subjected to general compound loading 408 § 128. Determination of normal stresses 410 1129. Determination of shearing stresses 413 130. Determination of displacements 414 131. Design of a simple crank rod 417 Chapter 24. Curved Bars 423 § 132. General concepts 423 § 133. Determination of bending moments and normal and shearing forces 424 § 134. Determination of stresses due to normal and shearing forces 420 § 135. Determination of stresses due to bending moment 427 § 136. Computation of the radius of curvature of the neutral layer in a rectangular section 433 § 137. Determination of the radius of curvature oi the neutral layer for circle and trapezoid 434 § 138. Determining the location of neutral layer from tables 436 § 139. Analysis of the formula for normal stresses In a curved bat 436 § 140. Additional remarks on the formula for normal stresses 439 § 141. An example on determining stresses in a curved bar 441 1 142. Determination of displacements in curved bars 442 § 143. Analysis of a circular ring 445 Chapter 25. Thick-walled and Thin-walled Vessels 446$ 144. Analysis of thick-walled cylinders 446
§ 145. Stresses in thick spherical vessels 453
§ 146. Analysis of thin-walled vessels 454

Chapter 26. Design for Permissible toads. Design for Limiting States 467

§ 147. Design for permissible loads. Application to statically determinate systems 457
§ 146. Design or statically indeterminate systems under tension or compression by the method of permissible loads 458
§ 149. Determination of limiting lifting capacity of a twisted rod 462
§ 150. Selecting beam section Tor permissible loads 465
§ 151. Design of statically indeterminate beams for permissible loads. The fundamentals. Analysis of a two-span beam 468
§ 152. Analysis of a three-span beam 472
§ 153. Fundamentals of design by the method of limiting states 474

PART VIII. Stability of Clements of Structures

Chapter 27. Stability ot Ban Under Compression 477

§ 154. Introduction. Fundamentals of stability of shape of compressed bars 477
6 155. Euler’s formula for critical force 480
§ 156. Effect of constraining the bar ends 484
§ 157. Limits of applicability of Euler’s formula. Plotting of the diagram of total critical stresses 488
§ 158. ‘The stability check of compressed bars 494
§ 159. Selection of the type of section and material 498
§ 160. Practical importance of stability check 502

Chapter 28. More Complicated Questions of Stability in Elements of Structures 604

§ 161. Stability of plane surface in bending of beams 504
§ 162. Design of compressed-bent ban 512
§ 163. Effect of eccentric compressive force and initial curvature of bar 517

PART IX. Dynamic Action of Forces

Chapter 29. Effect of Forces of Inertia. Stresses due to Vibrations 521

§ 164. Introduction 521
§ 165. Determining stresses in uniformly accelerated motion of bodies 523
§ 166. Stresses In a rotating ring (flywheel rim) 524
§ 167. Stresses in connecting rods 525
$168. Rotating disc of uniform thickness 529 1 169. Disc o f uniform strength 533 § 170. Effect of resonance on the magnitude of stresses 535 § 171. Determination of stresses in elements subjected to vibration 536 § 172. The effect of mass of the elastic system on vibrations 541 Chapter 30. Stresses Linder Impact Loading 548 § 173. Fundamental concepts 548 § 174. General method of determining stresses under impact loading 549 § 175. Concrete cases of determining stresses and conducting strength checks under impact 5S4$ 176. Impact stresses in a non-uniform bat 559 1177. Practical conclusions from the derived results 660
178. The effect of mass of the elastic system on impact 562
179. Impact testing for failure 565
180. Effect of various factors on the results of impact testing 568

§ 181. Basic ideas concerning the effect of variable stresses on the – strength of materials 571
§ 182. Cyclic stresses 573
§ 183. Strength condition under variable stresses 575
§ 184. Determination of endurance limit in a symmetrical cycle 576
1 185. Endurance limit in an unsymmetrical cycle 579
1 186. Local stresses 682
§ 187. Effect of size of part and other factors on endurance limit 589
emergence and development of fatigue cracks 593
§ 189. Selection of permissible stresses 597
§ 190. Strength check under variable stresses and compound stressed state 600
§ 191. Practical measures for preventing fatigue failure 602

Chapter 32. Fundamentals of Creep Analysis 605

§ 192. Effect of high temperatures on mechanical properties of metals 605
§ 193. Creep and after-effect 607
§ 194. Creep and after-effect curves 609
§ 195. Fundamentals of creep design 615
§ 196. Examples on creep design 620
Appendix 630
Name index 639
Su