KOTES ON RELATIVE MOTION. 



235 



Now, since ? =: Cwj — ^^ws, etc., it follows that 



_ =2(^0,3— M 

 B = 2 («wi — yws) ' 



0=2 (/3w2 — '^'^i) 

 a = I'm (ijC+ C^;) 



^ = (0—B)u>, — r'^, + ftu,, 



= ^6Ji + (-4 C) W2 '^'•'s 



Hence the above values for the component changes of moment of 

 momentum become 



A {i,, + ^0 - r («^2 + %) — /5 (<^3 + 63) + 2 (wi + Oi) (ro;3 — M 



— ('^2 + ^) L— i5,., + «r.2 -^(B — A) W3] — (a;3 + 63) [r<^i + 

 (^ _ C) 0,, — aa;3] — O3 [— r (^^i + °i) + ^ ('^2+ ^2) — « (^3 + 

 ^^3)] + ^2 [-/5 (a>: + ^) -a (a,^ +0^) + C (0,3 + O3)] 

 for the fii-st ; with similar expressions for the other two. 



