?= ^/Q2- 



M. Poinsot on the Percussion of Bodies. 277 



with an angular velocity 



_ Py 



and in the next place, we shall have a force equal and parallel to 

 the given force P, but applied at C, whose distance from the 

 centre of gravity G is x. We have seen that this force causes a 

 spontaneous rotation around a certain axis 0' Y' parallel to G Y, 

 and situated on the other side of the centre G at a distance 



X 



the angular velocity around this axis is 



P^ 



In virtue of the impulse given at C, therefore, the body tends 

 at one and the same time to turn around 0' X with the angular 

 velocity 



and around 0' Y' with the angular velocity 



Yx 



Hence, according to the principle of the composition of rota- 

 tions*, the body tends to turn around the diagonal of the rect- 

 angle constructed on the two lines O'jo and O'g' which represent 

 the rotations p and q. The given force P, therefore, gives rise to 

 a spontaneous axis of rotation which cuts the axis of x at the 

 distance 



X 



from the origin G, and is inclined to this axis at an angle whose 

 tangent is 



q _ a?x 



~p-~Wy' 



80 that, t and u being the current coordinates of this spontaneous 

 axis O'S, its equation will be 



or, more simply, 



Such, then, is the equation, between the coordinates t and u, 

 * TMorie nouvelle de la rotation des corps, 1" partic, art. 5. 



9= ^m- 



