\documentclass[a4paper,12pt]{article} %\input{mssymb} \begin{document} \baselineskip=24pt \vspace{-1cm} %\title{ERRATA} %\centerline{{\bf ERRATA}} %\author{J. Falnes} %\maketitle %\vspace{-1cm} \centerline{{\bf Comments, correction of errors and misprints etc. in}} \centerline{``{\it Topics on Extraction of Ocean-wave Energy: Various leftover lecture notes}'', May 2002.} \vspace{1cm} %\begin{abstract} %\end{abstract} %\pagebreak %\section{INTRODUCTION} \newcommand{\bdelta}{\mbox{\boldmath $\delta$}} \newcommand{\bDelta}{\mbox{\boldmath $\Delta$}} \newcommand{\bkappa}{\mbox{\boldmath $\kappa$}} \newcommand{\bpi}{\mbox{\boldmath $\pi$}} \newcommand{\bupsi}{\mbox{\boldmath $\upsilon$}} \newcommand{\bvec}{\left( \begin{array}{c}} \newcommand{\evec}{\end{array} \right)} \newcommand{\bmatr}{\left( \begin{array}{cc}} \newcommand{\ematr}{\end{array} \right)} \newcommand{\tr}{^{\rm T}} \vspace{-1cm} \noindent --------------------------------------------------------------------------------------------------- %\vspace{-1cm} \noindent Page 43, line 12: Reference to section D.8 could rather be a reference to Subsection 6.2.2 in OWOS (the textbook {\it Ocean Waves and Oscillating Systems}). \vspace{0.3cm} \\ \noindent Page 50, line 6 from bottom: Note that fig. K5 is on page 87. \vspace{0.3cm} \\ \noindent Page 69: Note that eqs. [P67] and [P68] correspond to eqs. (7.178) and (7.177), respectively, in OWOS. \vspace{0.3cm} \\ \noindent Page 73: Observe that eq. [P28] is the same as eq. (7.96) in OWOS. \vspace{0.3cm} \\ \noindent Pages 80 and 82: Observe that eq. [B75] is the same as eq. (4.136) in OWOS. \vspace{0.3cm} \\ \noindent Pages 81 to 82: Comment: The section ``K.5. Two-dimensional radiation damping matrix'' represents an extension of OWOS matter in Section 5.8 (OWOS pp. 179-181) to the case with OWCs included in the system of oscillators, in addition to the oscillating bodies. \\ \noindent Note also that the results of section ``K.5. Two-dimensional radiation damping matrix'' could have been obtained by application of OWOS matter in Section 7.2 for the two-dimensional case. \vspace{0.3cm} \\ \noindent Page 82: Note that the equation on the first line of page 82 is an extension of OWOS eq. (5.301) to the case with OWCs included in the system of oscillators, in addition to the oscillating bodies. \\ \noindent Thus eq. [P79] is an extension of an equation that would have resulted if the $h'$-s in eq. (5.301) were expressed by the $f'$-s by using eqs. (5.304) and (5.305). % %\noindent The last equation in section K.5 follows from eq (7.196) in OWOS. \vspace{0.3cm} \noindent --------------------------------------------------------------------------------------------------- \noindent Pages 68-103: Comment on notation. Comparison of matrices ${\bupsi}$, $\bpi$ and $\bDelta$ in OWOS, Section 7.2, with corresponding matrices ${\bkappa}$, $\bpi$ and $\bDelta$ in chapter K (pages 68-103 of ``Topics - - -''), where matrices are not denoted by bold-face symbols, but by a tilde ($\sim$) %(\vspace{0.2cm}$\tilde{ }$\vspace{-0.2cm} ) below symbols $\kappa$, $\pi$ and $\Delta$ (while transposed matrices are denoted by placing the tilde above symbols). \noindent In OWOS, eq. (7.101) defines the $N$-dimensional column vectors \noindent $ %\[ %\begin{equation*} \hat{\bupsi}=\bvec \hat{\bf u} \\ -\hat{\bf p}\evec \quad \mbox{and} \quad \hat{\bkappa}=\bvec \hat{\bf F} \\ -\hat{\bf Q} \evec %\nonumber %\label{ups_kap} %\end{equation*} %\] $ and eq. (7.91) the $N$-dimensional square matrix $%\begin{equation} {\bf \Delta}=\bmatr {\bf R} & -i{\bf J} \\ i{\bf J}\tr & {\bf G} \ematr %\bmatr R \ematr %{\bf \Delta}=\bmatr {\bf R} & -i{\bf J} \\ i{\bf J}\tr \ematr %\label{rdamp_mat} $%\end{equation} . Here the oscillating-body variables appear before the OWC variables. \noindent In contrast, in chapter K (pp. 68-103) the corresponding matrices used are defined as $ %\[ %\begin{equation*} \hat{\bpi}=\bvec \hat{\bf p} \\ \hat{\bf u}\evec \!\!\!\!\! \quad \mbox{,} \quad \hat{\bkappa}=\bvec \hat{\bf Q} \\ \hat{\bf F} \evec %\nonumber %\label{ups_kap} %\end{equation*} %\] $ and $%\begin{equation} {\bf \Delta}=\bmatr {\bf G} & -i{\bf J} \\ i{\bf J}\tr & {\bf R} \ematr %\bmatr R \ematr %{\bf \Delta}=\bmatr {\bf R} & -i{\bf J} \\ i{\bf J}\tr \ematr %\label{rdamp_mat} $%\end{equation} , however using tilde rather than bold face for matrix notation. Observe that not only has the order of $\hat{\bf p}$ and $\hat{\bf u}$, respectively of $\hat{\bf Q}$ and $\hat{\bf F}$, been interchanged, but also the minus sign have disappeared in the definitions of $\hat{\bf \bpi}$, respectively $\hat{\bf \bkappa}$. \vspace{0.3cm} \noindent --------------------------------------------------------------------------------------------------- \noindent For information to possibly confused readers: Note on the somewhat awkward labelling of equations in chapter K (pages 68-103): \noindent Let $\nu$ be a natural number. % %\noindent When an equation is labelled [K$\nu$], it is the same as equation (K$\nu$) in chapter K of the 1980 lecture notes (Falnes, J. and Iversen, L.C.: {\it Hydrodynamisk teori for b\o lgjekraftverk}, Institutt for eksperimentalfysikk, NTH, Universitetet i Trondheim, February 1980). \noindent When an equation is labelled [L$\nu$], it is an (including-OWCs) extension of equation (K$\nu$) in chapter K of these 1980 lecture notes, where only oscillating bodies, and no OWC, were considered in the oscillating system. \noindent When an equation -- on pp. 68-103 (but not on pp. 106-111(!)) -- is labelled [T$\nu$], it is a similar extension of equation ($\nu$) in the paper: Falnes, J.: Wave-power absorption by an array of attenuators oscillating with unconstrained amplitudes, {\it Applied Ocean Research}, Vol 6, No 1, pp 16-22, 1984. \vspace{0.3cm} \noindent -------------------------------------------------------------------------------------------------- \noindent Errata list %(http://www.phys.ntnu.no/$\sim\!\!$ falnes/topics2002corrections.pdf) %(http://www.phys.ntnu.no/${\mbox{\scriptsize {$\sim$}}}$falnes/topics2002corrections.pdf) (http://www.phys.ntnu.no/$\,\tilde{ }$ falnes/topics2002corrections.pdf) %(http://www.phys.ntnu.no/\~falnes/topics2002corrections.pdf) \noindent created 2002-10-19 (021019). \,\,\,\, Revised 021101 %/030000/... % 2002-05-03 %%% 16/2003-04-26 % etc. [as needed] \vspace{0.9cm} \noindent Readers who find additional errors or misprints, are encouraged to report by e-mail to \,\,\,\,\newline Johannes.Falnes@phys.ntnu.no \end{document}