# Elements of Theoretical Mechanics for Electronic Engineers

## 1st Edition

### International Series of Monographs in Electronics and Instrumentation

**Authors:**Franz Bultot

**eBook ISBN:**9781483151502

**Imprint:**Pergamon

**Published Date:**1st January 1965

**Page Count:**268

## Description

Elements of Theoretical Mechanics for Electronic Engineers deals with theoretical mechanics, which is considered one of the fundamental branches of instruction essential to training an engineer. This book discusses the oscillatory motions and their counterparts in electrical circuits and radio, and provides an introduction to differential operators of vector field theory. Other topics covered include systems and functions of vectors; dynamics of a free point; vibrations and waves; and statics. Worked examples and many notes on the application of most sections of the theories to electrical developments are also provided in this text. This publication is valuable to students taking a Higher National Diploma or Diploma in Technology, as well as students in the final year of the Higher National Certificate in electrical engineering.

## Table of Contents

Foreword to the English Edition

Foreword

Preface

1. Vectors-Vector Systems-Vector Functions

1.1. Vector

1.2. Scalar Product of Two Vectors

1.3. Vector Product of Two Vectors

1.4. The Moment of a Vector about a Point

1.5. The Moment of a Vector about a Straight Line

1.6. System of Sliding Vectors

1.7. Vector Fields

1.8. Couple

1.9. Reduction of a System of Vectors

1.10. Vector Function

1.11. Vector Derivative and Differential

1.12. Vector Derivatives of a Sum and of a Product of Vector Functions

1.13. Vector Integral

2. Kinematics of a Point

2.1. Characteristics of Curvilinear Motion

2.2. Characteristics of Rectilinear Motion

2.3. Some Important Rectilinear Motions

2.4. Some Important Curvilinear Motions

2.5. Velocity and Acceleration in Polar Coordinates

2.6. Tangential and Normal Components of the Acceleration

3. Dynamics of a Free Point

3.1. Fundamental Principles of Dynamics

3.2. Fundamental Equation of Dynamics

3.3. Systems of Units and Dimensional Equations

3.4. The Two Types of Fundamental Problems of Dynamics

3.5. Some Problems of the First Type

3.6. Some Problems of the Second Type

3.7. Theorem of Momentum

3.8. Applications of the Momentum Theorem

3.9. Theorem of Moment of Momentum

3.10. The Kinetic Energy Theorem

3.11. Applications of the Kinetic Energy Theorem

3.12. Central Force, Areal Velocity, Theorem of Areas and Binet's Formula

3.13. AppHcation of Binet's Formula—Determination of the Kinetic Energy of an Electron in a Stable Atom

4. Center of Mass—Dynamics of a Point Constrained in a Circular Trajectory—Moment of Inertia

4.1. Center of Mass or Center of Gravity of a System of Material Points

4.2. Center of Gravity of a Solid

4.3. The Dynamics of a Point Constrained to Move in a Circular Trajectory

4.4. Moment of Inertia of a Solid

4.5. Dynamical Equations of a Solid Turning about a Fixed Axis of Rotation

5. Vibrations and Waves

5.1. Undamped Linear Oscillation

5.2. Damped Linear Oscillation

5.3. Damped Linear Oscillation—Electrical Analogy

5.4. Forced Linear Oscillation

5.5. Forced Linear Oscillation—Electrical Analogy

5.6. Coupled Linear Oscillations

5.7. Coupled Linear Oscillations—Electrical Analogy

5.8. Equation of a Vibrating String

5.9. D'Alembert's Solution of the Equation of the Vibrating String

5.10. Interpretation of D'Alembert's Solution—Progressive Waves

5.11. Progressive and Stationary Sinusoidal Waves

5.12. Solution of the Vibrating String Equation by the Fourier-Bernoulli Method

5.13. Application of the Fourier-Bernoulli Solution to Stationary Waves in Radio Aerials

6. Scalar and Vector Fields

6.1. Scalar and Vector Fields—Definitions

6.2. Gradient of a Scalar Field Function

6.3. Divergence and Curl of a Vector Field Function

6.4. Flux of a Vector Field

6.5. Flux of a Vector Field—Application to Gauss's Theorem

6.6. Intuitive Idea of the Divergence

6.7. Circulation of the Vector Field—Intuitive Idea of the Curl

6.8. Divergence of the Position Vector, of a Gradient (Laplacian), of a Product and of a Curl

6.9. Application of the Divergence Operator—Energy Radiated by an Elementary Dipole

6.10. Curl of a Gradient

6.11. Field Deriving from a Potential

6.12. Field Deriving from a Potential—Applications

7. Statics

7.1. Conditions for Equilibrium of a System of Forces Applied to a Free or Bound Material Point without Friction

7.2. Conditions for Equilibrium of a System of Forces Applied to a Bound Material Point without Friction—Application to the Calculation of the Inclination of a Track

7.3. Conditions for Equilibrium of a System of Forces Applied to a Free Body or One Bound without Friction

7.4. Conditions for Equilibrium of a System of Forces Applied to a Free Body or One Bound without Friction—Applications

7.5. Conditions for Equilibrium of a System of Forces Applied to a Solid Constrained with Friction

7.6. Conditions for Equilibrium of a System of Forces Applied to a Solid Constrained with Friction—Applications

7.7. Equilibrium Configuration of a Heavy Homogeneous Cable Suspended between Two Fixed Points

7.8. Principle of Virtual Work

7.9. Applications of the Method of Virtual Work in Finding the Conditions for Equilibrium of a System of Forces Applied to a Solid Which is Held without Friction

Bibliography

Index of Electronic Topics Whose Mechanical Principles are Set out in the Text

List of Volumes Published in the Series in Electronics and Instrumentation

## Details

- No. of pages:
- 268

- Language:
- English

- Copyright:
- © Pergamon 1965

- Published:
- 1st January 1965

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483151502