subject to the initial conditions 



xgCe.O) = Bx(a(e),0) (16) 



yB(e,0) = By(a(e),0) (17) 



where a(e) is a prescribed function. 



In summary, we seek the solution of an initial-boundary value problem for 

 X = xp(e,t), y = yp(e,t), <\) = (t)p(e,t) on the free surface and x = xg(e,t), 

 y ~ yB^^'*^) °^ the body contour, in which e is a Lagrangian variable that 

 parameterizes the free surface and the body contour. These five functions 

 obey the evolution Equations (8), (9), (10), (14), and (15) subject to the 

 initial conditions (11), (12), (13), (16), and (17). The velocity potential 

 in these equations must satisfy Equation (2) subject to the Neumann boundary 

 conditions (3), (4), (5), and (6) and a Dirichlet boundary condition along the 

 free surface governed by Equation (8). 



The force on the body is calculated by integrating the pressure over the 

 wetted surface of the body. Because the flow problem is symmetric about 

 X = 0, the x-component of the force on the body vanishes: 



Fx = (18) 



The y-component of the force, positive upward, is given by 



Fy =-2 1 p(a,t) ny(a,t) (ds/da) da 



(19) 



where (n^ ,ny) is the unit normal at the body contour directed into the fluid 

 and s, increasing in the counterclockwise direction along the body, represents 

 arclength. Because of symmetry, the pressure is integrated over the half the 



