All-101 63 



analysis, the problem as deTined thus far might still have some 

 qualitative value. Unfortunately, for such a small value of &, 

 the terms in the equations of motion which involve a time- 

 derivative become very small, and we are wholly unjustified in 

 neglecting the non-linear terms while still retaining these 

 time dependent terms. 



In spite of these objections, the analysis for Problem 

 2 by the first method was carried through but the results were 

 not computed numerically. The analytical results are listed 

 in the next few pages, 



Ui = %o ^ ^%i' ^1 ^ ^10 -^ ^^11' % = %o ■" ^%1 



U2 = U20 + 6U23_, ^2 = ^20 ^ ^^21' ^2 = ^20 ^ ^^21 



1 

 Where U2o=V2o = by equation (4*$-) , U-[_q, V^^, H^^ are given by 



equations (-J. 22) , (-^ 23) and (4, 26) and the remaining values are 



given below, 



2 



= g. cos T(_^ + r - e ■^)r(©n^s^ + ii§^)sin nsy + | cos nsy] 



Q *- b D 



11 9 



2 . _.^_-l/3 



r/ -2/3 nsy'^. T - r a i (x-r)8 

 + a cos T sm nsyLCe - --^~-) — -r--^ + AJ e 



b9 3 



+ a cos T sin nsy e"^^^ j(l - ^^)x cos 2Li^il-_) 



2 

 + (l::IL§-l-.)JLsm (51ll5„^.) le ^ - a cos ^ n|Z_sin nsy • 



3 \/3 ? J ^b 



-1/3 

 - -1/3 -1/3 1/3'^ - ^e_ '-^ 



. r^cosCii^L-i— ^)+(-^^-^~ -l)^43ii(^y^g e 2 



P 2 3 /3 2 J -1/3 



+ a cos T sin nsyJc2 cos(^^*^-i|-— )+C3sin(^^ii— ^e 



