Muvthy 



and side hulls respectively, are known from design considerations, it 

 is not possible to separate the total inertia 



into separate components I— — J and 11 . 

 We thus obtain the set of equations : 



mcr ^ *nni = 2ir II /3P^ ex P * ( kx + y ) dxd Y 



e 001 



TTJpg // f , , . . ,_ /Id [<5h(x' , Z 1 )] j " 



° /fexp - kz' + l (kx +7 ) i — - — ^ Ll dx'd: 



5 1o 



mcr 2 z - pg A (z - x 9 ) - 4?ripg 



e 001 ^ 8 V 001 A 00l' k 



j/exp [-kz' + i(kx +7 )] a&h(x ^, Z ' )] dx'dz' + 

 + ^001 +h G W ll ^ 



dxdy = 

 x 



mh G ( % X 001 - g ^001 ) + (pgI A- m 2 gZ B "'e^^OOl " 

 " PgZ 001 Ax A + 47r k P _ S // eXp L' kz ' + i (kx +y } ] 



r^ .■ )i. x , a ph(»- .*■)]] dx , dz , + 



L dx' dz' 



+ 2(x ooi +h G d ooi } ffe*\ dxd y - ° 



s o 



(8-6) 



The first of the above equations gives the oscillatory surge 

 displacement explicitly. The left-hand side is actually the surge acce- 

 leration and this is independent of speed for the term a t which depends 

 upon the speed of motion is absent on the right-hand side. 



The other two equations enable the solution of the heave and 

 pitch oscillatory displacements. As before, these displacements are 



164 



