M. Poinsot on the Percussion of Bodies. 431 
GENERAL PROBLEM. 
2. A free solid body being animated by given forces, any one of 
its points C suddenly encounters a fixed point which compels the 
body to change its motion; required the direction and magnitude 
of the percussion which will be produced upon this obstacle. 
“8. The solution is not difficult to find; for if we represent the 
percussion on the fixed point by Q, it is evident that a force — Q) 
equal and contrary to Q, applied to the body at the moment of 
the shock, would at that moment precisely destroy the velocity 
of the point C. . 
In order to obtain the equations of the problem, therefore, it 
will suffice to express the condition that, under the influence of 
all the given forces, and of the unknown force —Q applied at the 
point C, this point of the body acquires a velocity equal to zero ; 
this sole condition being developed, will supply all that is neces- 
sary for the determination of the magnitude and direction of the 
required percussion Q. 
DEVELOPMENT OF THE SoLurion. 
4. Let us make the three principal axes of the body which 
pass through its centre of gravity G our coordinate axes; and 
represent by m the mass of the body; by ma*, m6, my” its 
three principal moments of inertia; and by 2, y, 2 the coordi- 
nates of the point C. 
The given forces may be reduced to three forces, 
Xo, Yo Lo, 
directed along the three axes, and to three couples 
Ig, Mo No 
in planes perpendicular to these axes. 
Similarly the unknown force —Q, applied at the point C, may 
be decomposed into three forces, 
XxX, Y, &, 
applied at the centre of gravity G and directed along the three 
axes, and into three couples around these axes, whose moments 
will be expressed by 
Yz—Zy, Z«e—Xz, Xy—Ya. 
5. The system of all the forces is thus reduced to the three 
forces 
X +X, YotY, 244, 
applied at the centre of gravity along the axes, and to the three 
couples 
L,+Zy—Yz, M)+Xz—Ze, Not Yx—Xy 
in planes perpendicular to these axes. 
