284 MISCELLANEOUS METHODS AND APPLICATIONS. [CHAP. XII. 



*251. Illustrative problem. Two uniform rods AB, EG of masses m lt 

 m z and lengths a, b are freely hinged at B, and AB can turn about A in a 

 vertical plane. The system starts from rest in a position in which AB is hori 

 zontal and EC vertical. To discuss the initial curvature of the path of any 

 point of EC. 



Let AB make an angle B with the horizontal, and EC an angle &amp;lt; with the 



Fig. 75. 



vertical at time t. Since B describes a circle of radius a about A, and since 

 the centre of inertia of EC describes a circle of radius $b relative to E, the 

 system of kinetic reactions will be as shown in the diagram. 



By taking moments about E for EC, and about A for the system, we 

 obtain the two equations 



a sn + - m 2 a cos 



= Jw^a cos 0+m 2 g (a cos + 16 sin 



Adding the equations, and dividing out common factors; we have 



+ 7712) ...... (1), 



and the first equation is 



^--ia0sin(0 + 0)-ia0 2 cos(0 + 0)=-^sin0 ......... (2). 



In the initial position = 0, = 0, = 0, = 0, and we have 



2 g 

 a 



In any position we have, by Maclaurin s theorem, 



also 0= 



Now, taking equation (2), we see that if were finite, &amp;lt;f&amp;gt; would be of order 

 t 3 , and of order 2 , so that the terms would be respectively of orders 1, 2, 2, 



. 



