# APPLIED GYRODYNAMICS

### CHAPTER I

```DEFINITIONS AND PRINCIPLES OF ELEMENTARY DYNAMICS
Translation and Rotation

1. Linear Motion: Definitions and Units
2. Angular Motion: Definitions and Units
3. Composition and Resolution of Forces
4. Composition and Resolution of Uniform Linear Velocities and Accelerations. Solved Problem
5. Composition and Resolution of Torques
6. Composition and Resolution of Angular Velocities, Accelerations and Moments
7. The Relation between the Angular Velocity of a Body and the Linear Velocity of any Point of the Body
8. The Relation between the Angular Acceleration of a Body and the Linear Acceleration of any Point of the Body
9. Centripetal and Centrifugal Forces
10. The Dynamic Vertical and the Dynamic Horizontal
11. Moment of Inertia
12. Values of the Moments of Inertia of Certain Bodies
13. Axes of the Principal Moments of Inertia of a Body
14. Centripetal Forces Acting on an Unsymmetrical Pendulum Bob
15. The Relation between Torque and Angular Momentum
16. Conservation of Angular Momentum
17. Centroid, Center of Gravity and Center of Mass

Simple Harmonic Motion
18. Simple Harmonic Motion of Translation
19. The Period of a Simple Harmonic Motion of Translation
20. Simple Harmonic Motion of Rotation
21. The Physical Pendulum
22. The Conical Pendulum
23. Wave Motions and Wave Forms
24. Phase and Phase Angle
25. The Mean Value of the Product of Two Simple Harmonic Functions of Equal Period
26. Oscillation of a Coupled System. Resonance
27. Damping of Vibrations
28. The Frahm Anti-Roll Tanks

THE MOTION OF A SPINNING BODY UNDER THE ACTION OF A TORQUE
29. Degrees of Freedom
30. The Effect on the Motion of a Spinning Body Produced by an External Force
31. Precession
32. Change in the Motion of a Ship Produced by Precession of the Shaft
33. Deviation of the Course of an Airplane Produced by Precessions of the Propeller Shaft
34-35. Magnitude of the Torque Required to Maintain a Given Precessional Velocity when there is Zero Motion about the Torque Axis, and when the Axes of Spin, of Torque and of Precession are Perpendicular to One Another. Solved Problems
36. The Direction and Magnitude of the Torque Developed by a Spinning Body when Rotated about an Axis Perpendicular to the Spin-Axis. Solved Problems
37. The Period of Precession
38. The Kinetic Energy of a Precessing Body
39. Nutation
40. The Effect of Hurrying and of Retarding the Precession of a Spinning Body
41. Motion of the Spin-Axis Relative to the Earth
42. The Angular Velocity of the Spin-Axle of an Unconstrained Gyroscope with Respect to the Earth. Solved Problem
43. An Instrument for Measuring the Crookedness of a Well Casing
44. The Weston Centrifugal Drier
45. The Effect on the Direction of the Spin-Axis of a Top Produced by Friction at the Peg
46. The Bonneau Airplane Inclinometer
47. The Sperry Airplane Horizon
48. The Drift of the Projectile from a Rifled Gun
49. The Effect of Revolving a Non-Pendulous Gyroscope with Two Degrees of Rotational Freedom, about the Axis of the Suppressed Rotational Freedom
50. The Pioneer Turn Indicator
51. The Clinging of a Spinning Body to a Guide in Contact with It
52. Components of the Torque Acting upon a Spinning Body Having one Fixed Point, Relative to the Three Coordinate Axes of a Rotating Frame of Reference
53. Components of the Torque Required to Maintain Constant Precession of a Body when the Precession Axis is Inclined to the Spin-Axis
54. The Griffin Pulverizing Mill. Solved Problem
55. The Automobile Torpedo
56. The Pendulum-Controlled Depth Steering Gear
57. The Conditions that Must Be Fulfilled by the Horizontal Steering Mechanism
58. The Bliss-Leavitt Torpedo Steering Gear
59. Method of Compensating the Effect of the Rotation of the Earth
60. Devices for Changing the Course of a Torpedo
61. Airplane Cartography
62. Direct Control of the Axis of a Camera
63. Indirect Control of the Axis of a Camera
64. Control of the Line of Sight of a Camera

THE GYROSCOPIC PENDULUM OR PENDULOUS GYROSCOPE
General Properties
65. The Gyro-Pendulum
66. The Period and the Equivalent Length of a Gyroscopic Conical Pendulum
67. The Inclination of the Precession Axis of a Gyroscopic Conical Pendulum to the Vertical
68. The Period of the Undamped Vibration, back and forth through the Meridian, of the Gyro-Axle of a Pendulous Gyroscope
69. The Torque with Which the Second Frame of a Gyroscope Resists	Angular Deflection
70. The Length of the Simple Pendulum Which Has the Same Period	as an Oscillating Body to Which is Attached a Spinning Gyroscope

Gyro-Horizontals and Gyro-Verticals
71. Determination of the Latitude of a Place
72. Gyro-Horizons
73. The Schuler Gyro-Horizon
74. The Anschutz Gyro-Horizon
75. The Bonneau-LePrieur-Derrien Gyro-Sextant
76. Fleuriais Gyroscopic Octant
77. The Sperry Roll and Pitch Recorder
78. The Sperry Automatic Airplane Pilot
79. The Sperry-Carter Track Recorder
80. Directed Gun-Fire Control
81. Gun-Fire Directorscopes

GYROSCOPIC ANTI-ROLL DEVICES FOR SHIPS
The Oscillation of a Ship in a Seaway
82.	The Rolling of a Ship due to Waves
83. The Pitching of a Ship due to Waves
84.	The Metacentric Height
85.	The Experimental Determination of the Metacentric Height
86.	The Period of the Rolling Motion of a Ship
87.	Methods of Diminishing the Amplitude of Roll

The Inactive Type of Gyro Ship Stabilizer
88. The Effect on the Motion of a Swinging Pendulum Produced by an Attached Gyroscope, (a) When the Precession of the Gyro-Axle is Opposed by a Frictional Torque
89. The Effect of a Spinning Gyroscope on the Rolling of a Ship
90. The Schlick Ship Stabilizer
91. The Fieux Ship Stabilizer

The Active Type of Gyro Ship Stabilizer
92. The Effect on the Motion of a Swinging Pendulum Produced by an Attached Gyroscope, (b) When the Gyro-Wheel is acted upon by a Torque about an Axis Perpendicular to the Spin-Axis and the Axis of Vibration of the Pendulum
93. The Sperry Ship Stabilizer
94. Operation of the Sperry Ship Stabilizer
95. The Braking System
96. Rolling of a Ship Produced by a Gyro
97. Admiral Taylor's Formula. Solved Problem

CHAPTER V
NAVIGATIONAL COMPASSES
The Various Types
98. The Altitude and Azimuth Method of Locating the Geographic Meridian
99. The Directive Tendency of a Magnetic Compass
100. The Deviations of a Magnetic Compass on an Iron Ship
101. The Deviation of a Magnetic Compass Produced by a Rapid Turn
102. The Earth Inductor Compass
103. The Magneto Compass
104. The Sun Compass
105. The Apparent Motion of the Spin-Axle of an Unconstrained Gyroscope Due to the Rotation of the Earth
106. The Meridian-Seeking Tendency of a Pendulous Gyroscope
107. The Meridian-Seeking Tendency of a Liquid-Controlled Non Pendulous Gyroscope
108. Making a Gyroscope into a Gyro-Compass
109. The Meridian-Seeking Torque Acting on a Gyro-Compass

The Natural Errors to Which the Gyro-Compass is Subject
110. The Latitude Error
111. The Error Due to the Velocity of the Ship. The Meridian-Steaming Error
112. The Deflection of the Axle of a Gyro-Compass Produced by Acceleration of the Ship's Velocity
113. The Period of a Gyro-Compass that will have Zero Ballistic Deflection Error when at a Particular Latitude
114. The Ballistic Damping Error
115. The Compass Error Due to Rolling of the Ship when on an Intercardinal Course. The Quadrantal or Rolling Error
116. Quadrantal Deflection Due to Lack of Symmetry of the Sensitive Element
117. The Suppression of the Quadrantal Error
118. The Degree of Precision of Gyro-Compasses

The Sperry Gyro-Compass
119. The Principal Parts of the Master Compass
120. The Follow-Up System
121. The Method of Damping
122. The Magnitude of the Latitude Error for which Correction Must Be made in the Sperry Gyro-Compass
123. Correction Mechanism for Velocity and Latitude Errors
124. Avoidance of the Ballistic Deflection Error
125. The Automatic Ballistic Damping Error Eliminator
126. Avoidance of the Quadrantal or Rolling Error
127. The Repeater System3

The Brown Gyro-Compass
128. Production of the Meridian-Seeking Torque
129. The Method of Damping
130. Absence of Latitude Error
131. The Meridian-Steaming Error
132. The Repeater System
133. The Ballistic Deflection Error
134. Prevention of the Quadrantal or Rolling Error

The Anschutz Gyro-Compass
135. The Sensitive Element of the Model of 1926
136. The Supporting System
137. Damping
138. The Meridian-Steaming Error
139. Prevention of the Ballistic Deflection Error
140. Avoidance of the Quadrantal or Rolling Error
141. The Follow-Up Repeater System

The Arma Gyro-Compass
142. The Sensitive Element
143. The Follow-Up System
144. The Course and Speed Error Corrector
145. Prevention of the Ballistic Deflection Error
146. Avoidance of the Ballistic Damping Error
147. Avoidance of the Quadrantal or Rolling Error

The Florentia Gyro-Compass
148. Arrangement of the Principal Parts of the Master Compass
149. The Follow-Up System
150. Damping
151. The Latitude and Meridian-Steaming Error Corrector
152. Avoidance of the Ballistic Error
153. Avoidance of the Error Due to Rolling and Pitching of the Ship When on Intercardinal Courses

GYROSCOPIC STABILIZATION
General Principles
154. Static and Kinetic Stability
155. The Stability of a System Consisting of a Body Capable of Oscillation and an Attached Precessing Gyro-Wheel
156. Some Laws of Dynamic Stability

Gyroscopically Stabilized Monorail Cars
157. The Economy of Monorail Cars
158. The Principles upon Which Depend the Dynamic Stabilization of Monorail Cars
159. The Effect of a Change in Linear Velocity on the Stability of a Monorail Car that Carries a Single Statically Unstable Gyroscope with Vertical Spin-Axle
160. The Effect of a Change in Linear Velocity on the Stability of a Monorail Car that Carries a Single Gyroscope with Horizontal Spin-Axle Transverse to the Car
161. Methods for Increasing the Kinetic Stability of a Monorail Car While the Car is Going Around Curves
162. The Schilovsky Monogyro Monorail Car
163. The Brennan Duogyro Monorail Car
164. The Scherl Duogyro Monorail Car of 1912
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