DYNAMIC SYSTEMS 



2/15 



simple pendulum swinging in a vertical plane. It is known that 

 the two variables — (x) angle of deviation of the string from 



Table 2/15/1. 



vertical, (y) angular velocity (or momentum) of the bob — are 

 such that, all else being kept constant, their two values at a 

 given instant are sufficient to determine the subsequent changes 

 of the two variables (Figure 2/15/1.) 



Figure 2/15/1 : Field of a simple pendulum 40 cm. long swinging in a 

 vertical plane when g is 981 cm. /sec. 2 , x is the angle of deviation from 

 the vertical and y the angular velocity of movement. Cross-strokes 

 mark the position of the representative point at each one- tenth second. 

 The clockwise direction should be noticed. 



An absolute system is thus ' state-determined ', and this is its 

 most important property : the occurrence of a state is sufficient 

 to determine the line of behaviour that ensues. The property 



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