KINEMATICS. [304. 



The component a x produces an infinitesimal angular velocity 

 a x dt about the axis Ox ; and hence gives to P the infinitesimal 

 velocities o, a x zdt, a x ydt along the axes Ox, Oy, Oz (see Art. 

 293); similarly, a y dt produces the velocities a y zdt, o, a y xdt, 

 and a z dt produces a z ydt, a z xdt, o. Collecting the terms paral- 

 lel to each axis and dividing by dt, we find the components of 

 the acceleration of P due to the angular acceleration a : 



ayZ-a z y, a,xa^ t a. y-a y x. (9) 



Finally, combining the corresponding terms in (8) and (9) and 

 remembering that a. x =da>Jdt, a y =da) y /dt, a z =da) z /dt, we find the 

 following expressions for the components of the total accelera- 

 tion j of the point P (x, y, z) : 



> 



at at 



^*-^s, (10) 



dco r dw.. 

 fy -*-x. 

 at at 



304. The formulas (10) for the components of the accelera 

 tion of any point (x y y, z) of a body rotating about a fixed poin 

 O can also be derived by differentiating the expressions (4) ir 

 Art. 293, which represent the components of the velocity o 

 such a point. It is only necessary, after the differentiation, tc 

 substitute for dxjdt, dy/dt, dz/dt their values from (4), Art 

 293, and to remember that cc? = co x 2 +a) y z -{-( t ) 2 2 . 



305. The complete study of the motion of a rigid body in th< 

 most general case, in particular the investigation of its accelera 

 tions, is beyond the scope of the present work. 



In addition to the works previously referred to, the following work 

 on kinematics may here be mentioned. 



An elementary introduction to kinematics, without the use "of the in 

 fmitesimal calculus, will be found in J. G. MACGREGOR, An elementary 



