# A Vector Approach To Oscillations

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A Vector Approach to Oscillations focuses on the processes in handling oscillations. Divided into four chapters, the book opens with discussions on the technique of handling oscillations. Included in the discussions are the addition and subtraction of oscillations using vectors; the square root of two vectors; the role of vector algebra in oscillation analysis; and the quotient of two vectors in Cartesian components. Discussions on vector algebra come next. Given importance are the algebraic and polynomial functions of a vector; the connection of vector algebra and scalar algebra; and the factorization of the polynomial functions of a vector. The book also presents graphical representations of vector functions of a vector. Included are numerical analyses and representations. The last part of the book deals with exponential function of a vector. Numerical representations and analyses are also provided to validate the claims of the authors. Given the importance of data provided, this book is a valuable reference for readers who want to study oscillations.

## Table of Contents

Preface

Chapter 1 The Technique of Handling Oscillations

1.1 Introduction

1.2 The Addition and Subtraction of Oscillations Using Vectors

1.3 Use of the Quotient of Two Vectors to Represent the Amplitude Ratio and Phase Difference of Two Oscillations

1.4 The Planar Product of Two Vectors

1.5 The Square Root of a Vector

1.6 The Planar Product of Two Vectors in Cartesian Components

1.7 The Quotient of Two Vectors in Cartesian Components

1.8 The Role to Be Played by Vector Algebra in

Oscillation Analysis

Summarizing Exercises

Chapter 2 Vector Algebra Using Planar Products and Quotients

2.1 Introduction

2.2 Algebraic Functions of a Vector

2.3 Polynomial Functions of a Vector

2.4 Factorization of Polynomial Functions of a Vector

2.5 Relation between Vector Algebra and Scalar Algebra

Summarizing Exercises

Chapter 3 Graphical Representation of Vector Functions of a Vector

3.1 Introduction

3.2 Contour Map for a Function Involving a Simple Zero

3.3 Contour Map for a Function Involving a Simple Pole

3.4 Cross Sections of Contour Maps

3.5 Cross Section of a Contour Map along the Reference Axis

3.6 Cross Section of a Contour Map along the Quadrature Axis

3.7 Behavior of a Function near a Pole or Zero

3.8 Analysis into Partial Fractions

3.9 Application of Partial Fraction Analysis

Summarizing Exercises

Chapter 4 The Exponential Function of a Vector

4.1 Introduction

4.2 Contour Map for the Exponential Function of a Vector

4.3 The Exponential Representation of a Unit Vector

Pointing in Any Direction

4.4 Relation between the Exponential Function and the Circular Functions

4.5 Importance of the Exponential Function for Relating Scalar and Vector Algebra

4.6 Analytical Properties of the Contour Map for the Exponential Function

4.7 The Concept of Actance

4.8 The Actance Diagram

4.9 The Concept of Vector Amplitude

4.10 The Concepts of Complex Amplitude and Complex Frequency

Summarizing Exercises

Problems

1. The Technique of Handling Oscillations

2. Vector Algebra Using Planar Products and Quotients

3. Graphical Representation of Vector Functions of a Vector

4. The Exponential Function of a Vector

5. Additional Problems

Subject Index

## Product details

- No. of pages: 160
- Language: English
- Copyright: © Academic Press 1965
- Published: January 1, 1965
- Imprint: Academic Press
- eBook ISBN: 9780323160889

## About the Author

### Henry G. Booker

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