Applied Analysis in Ship Hydrodynamics

This paper is written to pay tribute to the memory of my friend Ralph Kleinman. In 1962, I became aware of the original ideas in Ralph's early work when I was an engineering student in applied mathematics in Delft under supervision of professor Rein Timman. Ralph had just nished his doctor's thesis and Timman asked me to apply the same approach to a problem in the eld of transonic ows. Although we rst met in 1978 at the memorial meeting dedicated to Rein Timman, Ralph inuenced my early scientic interest. After we met our contact intensied, I stayed a few months in Newark and in Delft Ralph knocked on my door many times, mostly when I expected him to be far away. Luckily he always appeared before lunch time, so we could have a long conversation over a light lunch. It even could happen that we talked about mathematics. The last time Vicky and Ralph were in Delft, my student Lisette just nished her doctor's thesis on the topic of this paper. Therefore I have chosen this material. 1 Potential theory for ship motions In literature a variety of methods to compute the rst order potentials can be found. For zero forward speed the most commonly used method is based on the application of Green's theorem to the uid