Re: CrossProduct[ ]

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: CrossProduct[ ]*From*: keiper*Date*: Fri, 7 Aug 92 17:27:40 CDT*Cc*: bugs, emily, swolf

There seems to be a misunderstanding about CrossProduct[ ] in Calculus`VectorAnalysis`. In particular, when the default coordinate system is Cylindrical (or anything but Cartesian) this refers to the global coordinate system. Grad[ ] gives results in terms of the local, infinitesimal coordinate system which is NOT Cylindrical, but rather Cartesian. Thus when you use CrossProduct[ ] (or DotPrduct[ ] or ScalarTripleProduct[ ]) with vectors from the local, infinitesimal coordinate system, you need to specify that you are refering to a Cartesian coordinate system: In[1]:= <<Calculus`VectorAnalysis` In[2]:= SetCoordinates[Cylindrical] Out[2]= Cylindrical[r, theta, z] In[3]:= CrossProduct[Grad[r], Grad[theta], Cartesian] 1 Out[3]= {0, 0, -} r It could well be argued that this is a misfeature. Does one ever want to take the cross product of vectors in anything other than a Cartesian system? If so how often? Should the default be Cartesian with the ability to specify something else? I can easily change this, but it is not the sort of mathematics that I use and I don't know what the default should be. Jerry B. Keiper keiper at wri.com