164 M. Poinsot on the Percussion of Bodies. 



6. Thus upon the line drawn from the centre of percussion 

 through the centre of gravity, and on the opposite side of this 

 latter centre, there is always a point of the body which, during 

 the first instant, remains at rest, or in other words, receives no 

 motion whatever from the percussion appHed at C. The same 

 may be n$^ of all points of the line 01, drawn through par- 

 allel to the principal axis GZ. 



For an instant, therefore, the whole motion of the body re- 

 solves itself into a simple rotation around this line 01, just as if 

 the same were fixed ; this line 01 is called the spontaneous axis 

 of rotation, since it might be said that at the first instant the 

 body itself makes choice of the same. But as the only point of 

 this spontaneous axis which will here enter into consideration is 

 the point in line with the centres of gravity and percussion, 

 we shall refer to as the spontaneous centre of rotation. 



7. The point of the body which constitutes the spontaneous 

 centre of rotation has, therefore, a velocity equal to zero, and 

 during the instant under consideration the body turns around 

 this point. 



Since the centre of gravity has a velocity expressed by «^*, 

 and since a is the distance of G from 0, it follows that the body 

 has the same angular velocity 6 around the spontaneous axis 

 that it has around the centre of gravity G during the translation 

 of this centre through space. 



Hence any point whatever at the distance y from the spon- 

 taneous centre has the velocity yd ; for instance, the centre of 

 percussion C, at the distance a + h = l, has the velocity 16. 



It will be observed that the spontaneous centre is not, like 

 the centre of gravity G, a point which remains always the same 

 in the interior of the body : it changes every instant, or rather, 

 it is a new point of the body which, every successive instant, 

 becomes the spontaneous centre, just as it is a new point which 

 becomes the centre of percussion. In fact, since these two cen- 

 tres C and 0, together with the centre G, must necessarily be 

 situated on a right line perpendicular to the path described by 

 the centre of gravity, and at the constant distances h and a, 

 respectively, from this centre G, it is clear that during the move- 

 ment of the body C and describe, as it were, two circum- 

 ferences of circles around the centre of gravity whose radii are h 

 and a respectively, or, to speak more accurately, the several 

 points of these circumferences become, successively, the centres 

 of percussion and of spontaneous rotation. 



■p V V ah n ■ ah ~ 



