132 K. YE. Veselov and V. L. Panteleyev 



Here a is the deviation of the Cardan suspension from the direction of 

 the resultant force : the force of gravity plus the inertia! force developed 

 by the horizontal acceleration or the deviation of the Cardan suspension 

 from the direction of the instantaneous vertical, i.e. 



a"x 

 a == 9?; cos {pt + <5z) — cos [pt + d^^ = Oi^ax cos {pt + S), 



o 



where d which depends on d^, (5, is the phase of this deviation; a^^^ 

 is the amplitude of the deviation of the Cardan suspension from the instanta- 

 neous vertical. 



In marine pendulum devices this angle is registered by damped short 

 period pendulums. 



Bearing in mind what has been said previously, let us find an approximated 



. •• . ... (x^^ 



expression for ^q, disregarding sinusoidal terms of the order of ( — 



1 + — COS {pt +^z)+^- j(Po'- jn -J Omax . {2o) 



THE TANGENTIAL ACCELERATION 



In accordance with (18) and (20) the tangential acceleration component 

 •on the axis is 



- lo 9? = ^o[(pin^ cos {n^t + d-i) + (p2P^ cos {dt + d^)] (26) 



It is evident that this acceleration only yields terms the periods of which 

 are equal to the oscillatory periods of the Cardan suspension and the disturbing 

 accelerations. The periodic terms of frequency n^ can easily be separated 

 from the second term in brackets in expression (26) since the period of the 

 natural oscillations of the Cardan suspension differs from the period of the 

 accelerations. In addition, damping of the Cardan suspension enables one 

 to get rid of the influence of its natural oscillations. 



On the basis of the above we can replace (26) by 



- ^0 <? ^ ^oV2P^ cos {pt + 6^). (27) 



