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About CrossProduct


(*
  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

*)



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