Nonsinusoidal Osoillations of a Cylinder in a Free Surface 



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 coefficients for cylinders oscillating in a free surface," 

 Inst. Eng. Res. , University of California, Berkeley, 

 Series 82, Issue No. 16, i960, 181 pp. 



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APPENDIX A 



Description of the Boundary- Value Problems for the 

 Potentials <p^ for i = 1, 2, 3, 4, and 7 



The application of the perturbation expansions given by Eqs. 

 (17) and (18) to the exact boundary conditions given by Eqs. (12) and 

 (16) yields the following: 



On the free surface: 



^jy(x,0) - Kj^i =0 for i = 1 and 2, (A-1) 



where Kj = (rf/g, 



^jy(x,0) - 4Ki.2SPi = - J^ j ^i.2(X'0)(<'(i.2)yy ' ^i-z^d-rfy^ 



- 2(«>,^ ^ +?',^ ^ )f = h.(x) (A-2) 



^Mi-2)x Mi-2)y S ' 



for i = 3 and 4, and 



941 



