skew3.m

function [V,dV] = skew3(v)
%SKEW3		[V,dV] = skew3(v)
%		Takes a 3 components vector and calculates
%		the corresponding skew-symmetric matrix.
%		It is useful for implementing the vector
%		product of 3-vectors: v x u = skew3(v) * u
%
%		dV (optional) returns the 9x3 matrix which represents
%		the 3x3x3 tensor of derivatives of V wrt v. 
%		

%	Updated 8/30/93

V = zeros(3,3);
V = [[0,-v(3),v(2)]; [v(3),0,-v(1)]; [-v(2),v(1),0]];

if (nargout >=2),
	dV = [0  0  0 ; 
	0  0 -1 ;
	0  1  0 ;
	0  0  1 ;
	0  0  0 ;
	-1 0  0 ;
	0 -1  0 ;
	1  0  0 ;
	0  0  0 ];
end;

return;
%
%v = rand(3,1);	
%eps = 1e-6;
%for j=1:3,
%	vp = v;
%	vp(j) = v(j)+eps;
%	dVtest(:,j) = qtoQ(1/eps*(skew3(vp) - skew3(v)));
%end;
%
%return;
%
% difference test
%epsilon = 1e-6;
%csi = randn(3,1);
%rho = randn;
%for (k = 1:3),
%	csip = csi;
%	csip(k) = csip(k)+epsilon;
%	diff =  (skew3(csip)-skew3(csi))/epsilon;
%	diff = diff';
%	dFdcsi_test(:,k) = diff(:);
%end;
%[F,dFdcsi] = skew3(csi);