518 MB. A. E. H. LOVE ON THE SMALL FREE VIBRATIONS 



where the line-integral part is 



fck|2X(- -0"! + - - o- 2 ) + ^rss I 8w + f ds \2p. ( - <r 2 + " * ^ } + ACT I 8v. 

 J \m + n m + n 7 J \? + n m + n 7 



Again, 



= ff f i irlr s + i i^ 8 ^ a ^ + ff f- r^-^SiH- r is^&>&i^8 



JJ \ n,^p l ovC i "i^sPi d^/ JJ \ Ajpjd/Sdr l^h^p^of/ 



I 5~ I ~~ T~ 5 5*i ~t~ I 512 ) "r 5o I ~ IT 2 \o 37a i Oii ) " < * a ^P 

 JJ [_d \ Aj da dr A 2 p! df*/ dp \ n^opct'' p 3 of/ J 



. . (29) 



10. Collecting the terms, we have the differential equations of motion 

 m p_ _3_ AN / 



' Lrl \ 2/ \ 



n 



ft 



3- !* 



i T 



2nh 2-^- U- , 



d*[\hj\m+n * m + n 



3 /1W 2m , m-n \ 3 /w\l 



5~ (r )(- -<*s + - -o-i ^-i-^ (n = 



O a \ A 2/ \ m + ' TO + 71 V X 3/3 W/J 



f ^L . . 4 



L M 8 "*" a 



L JL' W 

 1P8 3/3 a 2 



4 j,, m Pi 3 /1\/ . 

 f 7i/i 8 - - ^ 2X, 



m + n [j> 2 3/3 kj/ \ 



TO . 



- K. 

 m 



o _\ 



h /> 8 a/9UA 2/fa ~ * 



\m 4- n 



r 3fl/2m ,m- \1 



2^^7-1- -0-0+- - <r, if 



L 3/3 1^ \m -f w r TO + n l /J 



. 3 /1\/ 2m . m \ 3/ra\"l ,., 



2 5s(r) (- -0-1 + - -- o-o A 2 =- ) = o, ..... (31) 



' 2 z 



