l^ 



^1 ^ 



Fig. 6 - Arrangement of the de - 

 vice in Fig. 3, with e = as the 

 angle of rotation, for determi- 

 nation of the coordinates of P 



a^ = (2R cos 2 61 + r cos 0) oP- 

 + (R sin 20 + r sin 6) e 



p, ; X 



^ 'f. 



a = R cos^oj^ + R sin^e 

 y 



a^ = - (2R sin 261 + r sind^ap- 



+ (R cos 2 61 + r cos 0) e . 



The speed of the mass becomes 



[r2 (1 + sin^0) + r^ + 2Rr cos6i]^/2 ^ 



For R = rand = -n, i.e., in P^ , we have 

 V = 0. 



(3) 



(4) 



Fig. 7 - Trajectory projec- 

 tions of the three coordinates 

 of P 



In the study of the dynamics of the point, 

 the principle of the conservation of energy is 

 often used. K we suppose that in the system 

 we are considering the energy remains con- 

 stant, we can derive an expression that may 



give us an indication about the way of varying a> and e to the varying of the 



ai^le . For this expression we can write: 



E = - mv^ 

 2 



Joj + pz = const- 



(5) 



1978 



