306 MOTION OF RIGID BODIES 



251. Let x, y, z be the coordinates of the center of gravity of 

 the rigid body, and let M be its total mass. Then 



etc. 



As the value of the 'remaining part of the left-hand member of 

 equation (127) we now have 



Mzv) 

 dt d>t 



= M-(yw-zv). 

 Thus equation (127) now assumes the form 



a) x = L. (128) 



If 2)x, 2)F, ^.Z denote the total components along the axes, 

 we have, by 180, the further equations 



* + =2 < 129 > 



Equations (128) and (129) and the two other pairs of equations 

 corresponding to the two other axes are the equations of motion 

 for a rigid body moving under any forces. 



o y * 



EULER'S EQUATIONS 



252. Let us now suppose that we have a second set of axes, 

 which we shall denote by 1, 2, 3. Let these axes move so as 

 always to retain the same position in the rigid body, the point 

 (which we have already supposed always to retain the same posi- 

 tion in the rigid body) being the origin. Let the axes 1, 2, 3 coin- 

 cide with the axes x, y, z at the instant under consideration. Then 

 the values of the coefficients of inertia referred to axes 1, 2, 3 are 

 the same as those referred to axes' x, y, z, namely A, B, C, D, E, F. 



