About CrossProduct

*To*: mathgroup at smc.vnet.net*Subject*: [mg8005] About CrossProduct*From*: sergio at scisun.sci.ccny.cuny.edu (Sergio Rojas)*Date*: Wed, 30 Jul 1997 23:57:59 -0400*Organization*: City College Of New York - Science*Sender*: owner-wri-mathgroup at wolfram.com

(* Hello: Regarding my post about the behavior of the Mathematica CrossProduct function, I found that that function seems to work in the following way: Given vectors A and B in Cylindrical coordinates, to find A cross B (AxB) the function CrossProduct first find AxB in Cartesian coordinates by transforming A and B to that coordinated system ( Cartesian), and then brings the result back to Cylindrical Coordinates. This seems to be the safest way of doing such computations. *) Needs["Calculus`VectorAnalysis`"]; AinCylindrical = {rho1, phi1, z1}; BinCylindrical = {rho2, phi2, z2}; AinCartesian = CoordinatesToCartesian[AinCylindrical, Cylindrical]; BinCartesian = CoordinatesToCartesian[BinCylindrical, Cylindrical]; AxBinCartesian = CrossProduct[AinCartesian,BinCartesian]; AxBinCylindrical = CoordinatesFromCartesian[AxBinCartesian, Cylindrical]; Print["Computations were done in ",CoordinateSystem," Coordinate system"] (* -------------------------------------- *) SetCoordinates[Cylindrical[r,phi,z]]; AxB = CrossProduct[AinCylindrical,BinCylindrical]; In[11]:= AxB == AxBinCylindrical Out[11]= True Print["These computations were done in ",CoordinateSystem," Coordinate system"] (* -------------------------------------- *) (* A literal, obviously wrong, interpretation of equation 2.11b, page 88, of Arfken's Mathematical Methods for Physicists, let me to the confusion. In any case, thanks very much to those of you that attempted clarify this point. Rojas E-mail: sergio at scisun.sci.ccny.cuny.edu *)