10 Stephenson, Nnv Type of Dynamical Stability. 



holds when the rod is supported by a double joint so that 

 it has complete freedom of motion about the vertical. 



4. The particular case of dynamical stability investi- 

 gated above is an example of a general type. If any 

 system fixed by one coordinate is statically unstable in a 

 position of equilibrium, that position is rendered stable by 

 the action of a periodic disturbance a[)plied in such a way 

 as to generate no motion about equilibrium. The main- 

 tenance of the stability here does not necessarily demand 

 an impressed motion : in the case of the inverted pendu- 

 lum, for example, a periodic variation in gravity would 

 have the same effect as the vertical oscillation of the 

 pivot. 



Some types of steady motion are also rendered stable 

 by a non-generating periodic disturbance* ; thus a top 

 rotating at a speed too low for stability is maintained 

 about the steady state by a vertical oscillation of the point 

 of support. 



It is possible that this method of ensuring the stability 

 of a steady motion may be of service in special cases 

 where the more usual devices are not applicable. In the 

 problem of mechanical flight the great difficulty lies in 

 obtaining longitudinal stability at slow speeds ; if an 

 aeroplane system is started in steady motion, a small 

 disturbance results in a pitching oscillation, which con- 

 tinues with increasing violence until finally the glider is 

 overturned. The mathematical investigation of the effect 

 of the non-generating periodic disturbance which is 

 illustrated in this paper, was undertaken with the view of 

 its possible application to a mechanism whereby stability 

 in gliding would be automatically ensured. In such a 

 case the motion is of a more complex character, involving 

 the interaction of several co-ordinates : it is hoped to give 

 a general examination of the problem later. 

 * loc. cit., g 2 and 3. 



