Gyrodynamics and Its Engineering Applications - 1st Edition - ISBN: 9780120638529, 9781483216140

Gyrodynamics and Its Engineering Applications

1st Edition

Authors: Ronald N. Arnold Leonard Maunder
eBook ISBN: 9781483216140
Imprint: Academic Press
Published Date: 1st January 1961
Page Count: 494
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Gyrodynamics and Its Engineering Applications deals with the engineering applications of gyrodynamics in a manner that stresses the physical concepts. Topics covered range from the kinematics of rigid bodies to frames of reference, along with moments and products of inertia. Gyro-verticals and the gyrodynamics of machines are also considered.

Comprised of 16 chapters, this book begins with a historical background on gyroscopes and an introduction to vectors, the kinematics of a particle, and rotating systems. The emphasis is on certain fundamental ideas governing the movement of bodies in three dimensions. Motion with respect to moving axes is discussed in detail, with particular attention to the intangible Coriolis acceleration. Subsequent chapters focus on the inertial characteristics of bodies and certain dynamical theorems; the motion of a free body and of a symmetrical gyroscope under gravity; gyroscopic vibration absorbers and stabilizers; the gyro-compass; suspensions for gyroscopes; gyro-verticals; and rate and integrating gyroscopes. The book also discusses inertial navigation as well as the whirling of shafts and aircraft gyrodynamics.

This monograph is intended primarily for engineers, but should also prove valuable to university teachers, research workers, and those who encounter gyroscopic problems.

Table of Contents

Chapter 1. General Introduction

1.1 History

1.2 Introduction to Vectors

1.3 Kinematics of a Particle

1.4 Newton’s Laws

1.5 Rotating Systems

1.6 Illustrative Examples

Chapter 2. Kinematics of Rigid Bodies

2.1 Products of Vectors

2.2 Translation and Rotation

2.3 Instantaneous Axis of Rotation

2.4 Finite and Infinitesimal Rotations

2.5 General Motion

Chapter 3. Frames of Reference

3.1 Transformation of Vector Components

3.2 Eulerian Angles

3.3 Moving Axes

3.4 Relative Motion

3.5 Illustrative Examples

Chapter 4. Moments and Products of Inertia

4.1 Definitions

4.2 Transformation Theorems and Principal Axes

4.3 Mohr’s Circle

4.4 Symmetric Bodies

4.5 Experimental Measurements

Chapter 5. Dynamical Theorems

5.1 Linear and Angular Momentum

5.2 General Equations of Motion

5.3 Equations of Motion for Rigid Bodies

5.4 Kinetic Energy

5.5 Lagrange’s Equations

5.6 D’Alembert’s Principle

Chapter 6. Motion of a Free Body

6.1 Introduction

6.2 The Solutions of Poinsot and Sylvester

6.3 Polhodes and Herpolhodes

6.4 General Solution

6.5 Axially-Symmetric Bodies

Chapter 7. Symmetrical Gyroscope Under Gravity

7.1 Introduction

7.2 Equations of Motion

7.3 Uniform Precession

7.4 Nutation

7.5 General Solution

Chapter 8. Gyrodynamics of Machines

8.1 Effects of Coriolis Forces

8.2 Spinning Discs and Rotors

8.3 Rolling Wheels and Discs

8.4 Grinding Mills

Chapter 9. Gyroscopic Vibration Absorbers and Stabilizers

9.1 Introduction

9.2 Historical Note

9.3 Gyroscopic Control of Forced Vibration

9.4 Gyroscopic Control of Self-Excited and Free Vibration

9.5 Stabilization of Ships

9.6 The Monorail

Chapter 10. The Gyro-Compass

10.1 Introduction

10.2 Foucault’s Directional Gyroscope

10.3 Principle of Action of the Gyro-Compass

10.4 Mechanical Arrangement

10.5 General Motion with Pendular Control

10.6 The Mercury Ballistic

10.7 General Motion with Mercury Ballistic

10.8 Errors

10.9 Effects at High Latitudes

Chapter 11. Suspensions for Gyroscopes

11.1 Introduction

11.2 Rotor Drives and Bearings

11.3 Single and Double Suspensions

11.4 The Cardan Suspension and Hooke’s Joint

11.5 Gimbal Errors

11.6 Dynamics of Gimbals

11.7 Effect of Flexibility of Rotor Shaft

11.8 Dynamics of a Platform Supported in Gimbals

11.9 Dynamics of a Rotor Driven by a Hooke’s Joint

Chapter 12. Gyro-Verticals

12.1 Introduction

12.2 The Gyro-Pendulum

12.3 Response to Vehicle Acceleration

12.4 Effect of Gimbal Bearing Friction

12.5 Response to Forced Vibration

12.6 Practical Gyro-Verticals

12.7 Response to Vehicle Acceleration

12.8 The Tilted-Axis Gyro-Vertical

12.9 Mechanical Design

12.10 Schuler Tuning of a Gyro-Pendulum

Chapter 13. Rate and Integrating Gyroscopes

13.1 Introduction

13.2 Single-Axis Rate Gyroscopes

13.3 Aircraft Turn-and-Slip Indicator

13.4 Floated Single-Axis Gyroscopes

13.5 A Two-Axis Rate Gyroscope

13.6 An Integrating Gyro-Accelerometer

13.7 A Vibratory Rate Gyroscope

Chapter 14. Inertial Navigation

14.1 Principles

14.2 Navigation Around a Fixed Sphere

14.3 Motion Around a Rotating Sphere

14.4 An Inertial Navigating System

14.5 Instrument Errors

14.6 Geophysical Effects

14.7 Stabilized Platforms

Chapter 15. Gyroscopic Effects in the Whirling of Shafts

15.1 Introduction

15.2 Shaft with a Single Disc

15.3 Shaft with Several Discs

15.4 Shaft with Many Discs

15.5 Shaft with a Single Unsymmetrical Body

Chapter 16. Gyroscopic Effects in Aircraft

16.1 Introduction

16.2 Rotors and Propellers

16.3 General Dynamics of Aircraft

16.4 Gyroscopic Coupling of Aircraft Oscillations

16.5 Aircraft in Steady Roll

16.6 Application to Missiles

16.7 Helicopter Rotors


A. The Operator D

B. The Second-Order Equation of Vibration Theory

C. Routh-Hurwitz Stability Criteria


Answers to Problems



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© Academic Press 1961
Academic Press
eBook ISBN:

About the Author

Ronald N. Arnold

Leonard Maunder