16. APPLICATIONS OF THE GYROPENDULUM 



W. S. von Arx 



1. Introduction 



From a ship at sea the confusion of horizontal accelerations prevents men 

 and most instruments from being able to detect in any precise way the direction 

 of local gravity. The bob of an ordinary pendulum tends to lag behind the 

 motion of its point of support as it is accelerated. Only under conditions of rest 

 will the center of mass of a short pendulum lie exactly and continuously on a 

 vertical line beneath its point of support. 



But if the earth is approximated by a non-rotating sphere and it is con- 

 sidered that the pivot point of a simple pendulum is moving along a great 

 circle at some slow, constant speed, it is apparent, once the initial oscillations 

 have been damped out, that the line connecting the pivot point with the center 

 of mass of the pendulum can be extended to intersect the geocenter at all times. 

 As seen from inertial space this requires the rest point of the pendulum to 

 execute one rotation around the pivot for each revolution of the pivot around 

 the circumference of the great circle. 



It was shown by M. Schuler in 1923 that if, on a non-rotating spherical earth, 

 a physical pendulum is allowed to align itself with local gravity, the direction 

 of the line joining the center of mass and the point of support will always 

 coincide with the direction toward the earth's center, regardless of horizontal 

 accelerations, if its period of oscillation is 84 min. A physical pendulum with a 

 period of 84 min is equivalent to a simple pendulum having a length equal to 

 the mean radius of the earth. With the bob, in effect, at the geocenter, the 

 point of support can be moved in any arbitrary way over the curve of a non- 

 rotating spherical earth with the results that Schuler described. 



A difficulty with Schuler's suggestion is that any practical physical pendulum 

 with a period near 84 min has its center of mass separated from the point of 

 support by the same order of distance as the unit-cell dimensions separating the 

 atoms of the material of which the pendulum is composed. 



2. The Gyropendulum 



Schuler's ideal system can still be realized if a gyrating mass is substituted 

 for the inert mass of the pendulum bob. A gyropendulum with its rotating 

 member spinning about an axis passing through the pivot point transforms the 

 inert mode of pendulum oscillation in a plane into a conical motion about the 

 vertical. The precessional period of a gyropendulum can be made very long in 

 comparison with its period as an inert physical pendulum. 



If r is the radius of the gyration of the rotor, S the angular speed of the rotor, 

 L the distance from the pivot to the center of mass of the gyropendulum and g 

 the acceleration due to gravity, the period of oscillation, T, of the system is 



9 



[MS received June, 1960] 325 



