CalcPertAreaChange(a,b,s,Z0_start)

function del_area = CalcPertAreaChange(a,b,s,Z0_start)
%  Version: 1.0, 19 March 2008
%
%  Calculates area change of Kirchhoff vortex due to perturbation

        x_n = a*cos(s); y_n = b*sin(s);
        X = x_n(find(y_n >= 0));
        Y = y_n(find(y_n >= 0));
        F = @(x)interp1(X,Y,x, 'spline');
        area_null = -2 * quadl(F,X(1),X(end));  

        x_pert = real(Z0_start); y_pert = imag(Z0_start);
        X = x_pert(find(y_pert >= 0));
        Y = y_pert(find(y_pert >= 0));
        F = @(x)interp1(X,Y,x, 'spline');
        area_pert = -2 * quadl(F,X(1),X(end));
        del_area = area_pert / area_null;
        disp(['area change due to perturbation: ', num2str(del_area)]);