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.

Contenu

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
Appendices
A. The Operator D
B. The Second-Order Equation of Vibration Theory
C. Routh-Hurwitz Stability Criteria
Problems
Answers to Problems
Index