242, 243] 



RIGID BODIES UNDER IMPULSES. 



275 



*243. Impulsive motion of connected systems. In illus- 

 tration of the application of the equations of impulsive motion to 

 systems of rigid bodies with invariable connexions we take the 

 following problems. In the first it will be observed that we do 

 not need to introduce explicitly the reactions between the connected 

 bodies. The second illustrates the choice of equations ; for, although 

 some of the unknown reactions must be introduced, it is unnecessary 

 to form equations for each body separately. 



I. Three uniform rods of masses proportional to their lengths are freely 

 jointed together and laid out straight, and one of the end rods is struck at the 

 free end at right angles to its length. It is required to find how they begin to 



move. 



Let 2a, 26, 2c be the lengths of the rods, the last being struck, and let 



PA 



Fig. 71. 



xja, yjb, z/c be the angular velocities with which they begin to move, u the 

 velocity of the centre of inertia of the first. Then the system of velocities 

 is as shown in the figure. Let P be the impulse applied at the end A, and 

 *a, Kb, KG the masses of the rods. 



We take moments about C for the rod CD, about B for the rods EC, CD, 

 and about A for the three rods, and we resolve for the whole system at right 

 angles to the rods. We thus obtain the equations 



Subtracting the second and third we get, on dividing by c, 

 e(t*+# +%+f) +26 (+#+y)+2aw-0, 



and, on simplifying this and the second by using the first, we get 

 # 



and 



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