. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. 301 T. H. Havelock M'gialSf. The motion of the spheroid is made up of a linear velocity hO. parallel to Cx and a rotation D. about Cz. In terms of spheroidal co-ordinates given by x = aeii^, 2/ = ae(l-/*2)i(S'-l)*cosw, 2 = ae(l-/i2)i(^2^ l)4sinw, (21) the known solution for this motion in an infinite liquid is (Lamb 1932) 95 = 2AaehQAP^{lx) Q^{Q - ^Ba^emPUfi) QUO cos w, (22) with ^-i = 2e/(l-e2)-log{(l + e)/(l-e)}, | B-i = {3(2-e2)/e2}log{(l + e)/(l-e)}-2(6-7e2)/e(l-e2).J It is well kno
. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. 301 T. H. Havelock M'gialSf. The motion of the spheroid is made up of a linear velocity hO. parallel to Cx and a rotation D. about Cz. In terms of spheroidal co-ordinates given by x = aeii^, 2/ = ae(l-/*2)i(S'-l)*cosw, 2 = ae(l-/i2)i(^2^ l)4sinw, (21) the known solution for this motion in an infinite liquid is (Lamb 1932) 95 = 2AaehQAP^{lx) Q^{Q - ^Ba^emPUfi) QUO cos w, (22) with ^-i = 2e/(l-e2)-log{(l + e)/(l-e)}, | B-i = {3(2-e2)/e2}log{(l + e)/(l-e)}-2(6-7e2)/e(l-e2).J It is well known that the hnear motion can be expressed in terms of a certain source distribution along the axis of the spheroid, and it can easily be shown that the angular motion can be ascribed to a doublet distribution along the axis. In fact, (22) is equivalent to 4> = AhQ. 1: kdk ^ k.{ah^-k^)dk (24) ^^{(x-kr + if + z^}i ^j_^{{x-kf + y^ + z^}^- We may now obtain the required solution by integration of the expression for a source given in (6). For the first term in (24) we have to replace a typical factor JniKh) cos n(6 - Qt) in (6) by JJ^Ki^^ + ^^)*} cos n{d a), where tan a = kjh; and, taking account of the integration in k, this may be replaced by Jn{K{h^ + k^)^} sin no, sin n{6 - Qt). Further, so far as the co-ordinates x, y, z are concerned, the second term in (24) may be derived by taking djdy of the first term; and when the expressions are put in terms of the fixed co-ordinates this is equivalent to operating by didh. Also we have ^[JX/i2 + P)i}sinna] = i/c[J„_i{/c(;i2 + ^2)i} sin (w - 1) a - Jn+i{K(h^ + k^)^} sin (w + 1) a]. (25) 558. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Havelock, Thomas, Sir, 1877-. Washington, Office of Naval Research, Dept. of the Navy; for sale by the Superintenden
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Keywords: ., bookcentury1900, bookcollectionbiodive, booksubjecthydrodynamics
