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• Derivative Seakeeping Quantities
  ...ial}{\partial X} \right) \left( \phi_3 + \phi_5 \right) + \left( i\omega - U \frac{\partial}{\partial x} \right) \left( \phi_I + \phi_D \right) + g \lef
  3 KB (530 words) - 09:12, 16 October 2009
• Mittag-Leffler Expansion for the Floating Elastic Plate Dispersion Relation
  R\left( q_n\right) =\frac{\omega^{2}q_n}{\omega^{2}\left( 5q_n^{4}+u\right) For the sake of simplicity, write <math>u=1-m\omega^{2}</math>. When <math>Im
  20 KB (3,424 words) - 12:02, 11 December 2009
• Introduction to KdV
  \partial _{t}u+6u\partial _{x}u+\partial _{x}^{3}u=0. u\left( x,t\right) =f\left( x-ct\right)
  8 KB (1,306 words) - 03:57, 10 August 2023
• Wave Energy Density and Flux
  We require the following <u>Lemma</u> which is easily proved. If ...al\Omega_U </math> the fluid boundaries moving with velocity <math>\mathbf{u}</math> relative to an earth frame.
  16 KB (2,666 words) - 17:44, 23 February 2011
• Wave Momentum Flux
  <u> Proof </u>: ...><math> \frac{\mathrm{d}M_x}{\mathrm{d}t} = - \int_{-h}^{\zeta} ( P + \rho u^2 ) \mathrm{d}z </math></center>
  14 KB (2,268 words) - 08:26, 2 January 2019
• Linear and Second-Order Wave Theory
  ...the body boundary condition at <math> U=0 </math> (zero speed) and <math> U>0 </math> (forward speed).
  9 KB (1,336 words) - 09:03, 17 July 2019
• Standard Notation
  * <math>U</math> is the forward speed
  5 KB (842 words) - 19:59, 26 July 2012
• Two Semi-Infinite Elastic Plates of Identical Properties
  If &phi; and &psi; are both twice continuously differentiable on ''U'', then \oint_{\partial U} \left( \psi {\partial \varphi \over \partial n} - \varphi {\partial \psi \
  22 KB (4,078 words) - 05:36, 10 May 2010
• Interaction Theory for Infinite Arrays
  \sum_{m=-\infty}^\infty \int_{-\infty}^{\infty} f(u)\, \mathrm{e}^{-\mathrm{i} mu} \,\mathrm{d} u= 2\pi \sum_{m=-\infty}^\infty f(2m\pi).
  14 KB (2,538 words) - 08:21, 19 October 2009
• Free-Surface Green Function for a Floating Elastic Plate
  R\left( q_n\right) =\frac{\omega^{2}q_n}{\omega^{2}\left( 5q_n^{4}+u\right) R\left( q_n\right) =\frac{\omega^{2}q_n}{\omega^{2}\left( 5q_n^{4}+u\right)
  17 KB (2,953 words) - 16:40, 8 December 2009

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