Gyrodynamics and Its Engineering Applications

Gyrodynamics and Its Engineering Applications

1st Edition - January 1, 1961

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  • Authors: Ronald N. Arnold, Leonard Maunder
  • eBook ISBN: 9781483216140

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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


Product details

  • No. of pages: 494
  • Language: English
  • Copyright: © Academic Press 1961
  • Published: January 1, 1961
  • Imprint: Academic Press
  • eBook ISBN: 9781483216140

About the Authors

Ronald N. Arnold

Leonard Maunder

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