Cagemine

Hi, I am seeking advice, direct or indirect (link to helpful resources), on transforming bending moments from local to global coordinate system using 3-D permutation tensor. For example, I have a series of bending moments acting on a node but in a local coordinate system and I want to transform these to the global coordinate system. From my reading on this the 3-D permutation tensor is used in conjunction with a function for the local bending moments and transforms them into global bending moments at that node. Global coordinate system [1 0 0 ; 0 1 0 ; 0 0 1] Local coordinate system [ 0.707 0.707 0 ; -0.707 0.707 0 ; 0 0 -1] A vector P <px, py, px> represents the beam and is parallel to the global X-axis, P = < 1 0 0 > The following local bending moments are applied (counter clockwise positive) Moment about local x-axis, mx = 0 units Moment about local y-axis, my = 2 units Moment about local z-axis, mz = 0 units What are the resulting global moments. The general formula used is: M1i = εjik [mz1 pk y1j - my1 pk x1j + mx (x1j y2k - y1j x2k)/2] 1 or 2 mean the near or far ends of a beam ijk take the form of 1,2,3 (representing x,y,z) I have determined the answer to be: Moment about global X-axis, Mx = -1.41 units (anti cyclic permutation) Moment about global Y-axis, My = 1.41 units (cyclic permutation) Moment about global Z-axis, Mz = 0 units I have an issue with my understanding of the 3-D permutation tensor. Thus my true question being, How does one determine what the permutation should be, cyclic (123) or anti-cyclic (321) in this Cartesian coordinate axis environment? Regards, Cage