The Lorentz Reciprocal Theorem
The Lorentz Reciprocal theorem, first written down by H. A. Lorentz in 1896 , is a very general theorem in low Reynolds number hydrodynamics, relating the stress and velocity fields on an arbitrary surface. I will first derive the reciprocal theorem, and then discuss some modern applications of the theorem, in particular to the calculation of the propulsion speed of swimmers with defined tangential velocity fields, known as squirmers.
 H.A. Lorentz, Eene algemeene stelling omtrent de beweging eener vloeistof met wrijving en eenige daaruit afgeleide gevolgen. Zittingsverslag van deKoninklijke Akademie van Wetenschappen te Amsterdam 5 (1896) 168-175.
English translation by K.K. Kuiken: H.A. Lorentz, A general theorem on the motion of fluid with friction and a few results derived from it. Journal of Engineering Mathematics 30 (1996) 19-24.
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