The Motion of a Ship As a Floating Rigid Body in a Seaway
The Motion of a Ship As a Floating Rigid Body in a Seaway
James Johnston Stoker
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The bcundrr-y ccnditicns (3. 3o) and (3. 37/ show th'-. T ^ d^^pends -. N o (t), ^. -j_(t) and Q^-^{t), The potential prcbl-m can theoretic ally be solved f-r /-, in the form 1 ^1 " /■^[^, y, -^, t; i. J^Jt), Q^_At), Q.^-^it)] without using (3. 29), (3. 3'^), (3. 32). The significance oT this has already been disousijed in ;'ioc. 1 ii: relation t^'. Equati. I- (l. LL|-). The gen^^ral procedure t- h^ foll'wed in s-. , lving all pr. Bleras was all discussed there. The general potential problem de...fined above vjIII be thu sub- ject cf a separate study. The remainder of this paper is c- ncerned with the special case of a ship ijhich moves along a straight course into waves whose crests are at right angles t-. The course. For this case there are surging, heaving and pitching motions, but 9, = C, 9^ = 0, I'o = anrl the TDotential function / is an even functitn of z. "Jnr'er these conditions the equations of motion are xre simple. They are (3. 36) li 2, = 2pjh^(/ -s^/ JdA + T (3. 39) 'A^A = -2pgyJhdx-2pg9^Jxlidx+2i:.
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