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.
Author(s): Booker, Henry G.
Publisher: Academic Press
Year: 1965
Language: English
Pages: 157
City: New York
Preface
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 ofTwo Vectors in Cartesian Components
1.8. The Role to Be Played by Vector Algebra in Oscillation Analysis
Summarizing Exercises
2. Vector Algebra Using Planar Products and Quotients
2.1. Introduction
2.2. Algebraic Functions of a Vector
2.3. Polynominal Functions of a Vector
2.4. Factorization of Polynomial Functions of a Vector
2.5. Relation between Vector Algebra and Scalar Algebra
Summarizing Exercises
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 Involvinga 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. Beh avi or of a Function near a Poi e or Zero
3.8. Analysis into Partial Fractions
3.9. Application of Parti al Fraction Analysis
Summarizing Exercises
4. The Exponential Function of a Vector
4.1. Introduction
4.2. Contour Map for the Exponential Functionof 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 ofVector Amplitude
4.10. The Concepts of Complex Amplitude and Complex Frequency
Summarizing Exercises
Problems
Index
