Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1997
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

Wrong behavior of CrossProduct

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7958] Wrong behavior of CrossProduct
  • From: sergio at scisun.sci.ccny.cuny.edu (Sergio Rojas)
  • Date: Fri, 25 Jul 1997 02:40:32 -0400
  • Organization: City College Of New York - Science
  • Sender: owner-wri-mathgroup at wolfram.com

(* Hello fellows:

   After playing a little bit with the Mathematica construction for the cross
   product of two vectors, implemented by the function CrossProduct of the
   package VectorAnalysis, I strongly believe that CrossProduct do not
   work properly on Mathematica ... *)

In[1]:= $Version
Out[1]= DEC OSF/1 Alpha 2.2 (September 9, 1994)

In[2]:= Needs["Calculus`VectorAnalysis`"];
In[3]:= V = {a1,a2,0};
In[4]:= U = {0, 0, 1};

In[5]:= CrossProduct[U,V]
Out[5]= {-a2, a1, 0}
                      	(* This result is correct *)
In[6]:= CoordinateSystem
Out[6]= Cartesian
			(************ Quit and start again ************)

In[1]:= Needs["Calculus`VectorAnalysis`"];
In[2]:= SetCoordinates[Cylindrical[r,phi,z]];
In[3]:= V = {a1,a2,0};
In[4]:= U = {0, 0, 1};
In[5]:= CrossProduct[U,V]

                2        2     2        2
Out[5]= {Sqrt[a1  Cos[a2]  + a1  Sin[a2] ], 
 
>    ArcTan[-(a1 Sin[a2]), a1 Cos[a2]], 0}

In[6]:= PowerExpand[Simplify[%]]
Out[6]= {a1, ArcTan[-(a1 Sin[a2]), a1 Cos[a2]], 0}

In[7]:= ?ArcTan  
ArcTan[z] gives the inverse tangent of z. ArcTan[x, y] gives the inverse
   tangent of y/x where x and y are real, taking into account which quadrant
   the point (x, y) is in.


	(* Using Mathematica definition for ArcTan[x, y], Out[6] can be 
           rewritten as {a1,-ArcTan[Cot[a2]],0}. This answer is obviously
           wrong as far as the Cross Product of V and U concern *)
 
In[7]:= CoordinateSystem
Out[7]= Cylindrical

			(************ Quit and start again ************)

In[1]:= Needs["Calculus`VectorAnalysis`"];
In[2]:= SetCoordinates[Spherical[r,theta,phi]];
In[3]:= V = {a1,a2,0};
In[4]:= U = {0, 0, 1};
In[5]:=  CrossProduct[U,V]
Out[5]= {0, 0, 0}
	         (* Again, wrong result. Same results were obtained on *)
In[1]:= $Version
Out[1]= SPARC 2.2 (December 15, 1993)

Rojas

E-mail: sergio at scisun.sci.ccny.cuny.edu



  • Prev by Date: subscripts in function definitions
  • Next by Date: Help: Implicit 3D-Plot
  • Previous by thread: Re: subscripts in function definitions
  • Next by thread: Re: Wrong behavior of CrossProduct