# Magnetic Positioning Equations

## 1st Edition

### Theory and Applications

Authors:
Paperback ISBN: 9780123985057
eBook ISBN: 9780123985064
Published Date: 29th June 2012
Page Count: 112
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## Description

In the study of Magnetic Positioning Equations, it is possible to calculate and create analytical expressions for the intensity of magnetic fields when the coordinates x, y and z are known; identifying the inverse expressions is more difficult. This book is designed to explore the discovery of how to get the coordinates of analytical expressions x, y and z when the intensity of the magnetic fields are known. The discovery also deals with the problem of how to analyze, define and design any type of transmitter along with its positioning equation(s).

## Key Features

• Presents new simple mathematical solution expressions.
• Describes how to solve analytically the 6D systems filing
• Defines practical multiple turns coil transmitters and their positioning equations
• Uses optimization methods with positioning equations to improve the sensitivity problem
• Presents more theoretical approach to define magnetic positioning equations

Researchers in physics and engineering, mathematicians, engineers, companies developing trackers

Preface

Chapter 1. Introduction

Chapter 2. Magnetic Fields

2.1 Single-Wire Magnetic Field

2.2 Magnetic Geometric Factor (G)

2.3 Magnetic Field of Triangular Wires

Chapter 3. First Magnetic Positioning Equation

3.1 Resolving Factor G

3.2 Triangular Couple

3.3 Multiple-Turn Coils

Chapter 4. Magnetic Positioning System

4.1 Detector Rotation Matrix

4.2 Solution of the Rotation Matrix

4.3 Detector Coordinates

Chapter 5. Equations of Quadrilateral Coils

5.2 Angle Rotation Coils

5.3 Coil Design

5.4 ARC Coils – Triple Quadrilaterals

5.5 XYZ Coils – Quadrilateral Symmetric Triple

6.1 Real ARC Quad Coil Design

6.2 Real XYZ Coil Design

6.3 Manipulation Properties

Chapter 7. Distortions and Disturbances

Optimal Estimation Methods

7.1 Scan System for ARC Coils

7.2 Scan System for XYZ Coils

7.3 G Distances

7.4 Vertex Problem

Chapter 8. Detectors

8.1 Energy Detectors

8.2 Detector Coils

Chapter 9. Coefficients Method

9.1 Ten Steps to Positioning Equations

9.2 Examples

9.3 Two-Axis Detector Positioning Equations

Chapter 10. Positioning Equations – 3D Coils

10.1 3D Triangles

10.3 3D Coefficient Method

10.4 One-Axis Detector Positioning Equations

Open Issues

APPENDIX A: Quadratic to Quartic Equations

APPENDIX B: Matrix Structure

No. of pages:
112
Language:
English
Published:
29th June 2012
Imprint: