Re: Dot Product in Cylindrical Coordinates

*To*: mathgroup at smc.vnet.net*Subject*: [mg69276] Re: Dot Product in Cylindrical Coordinates*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Tue, 5 Sep 2006 05:30:40 -0400 (EDT)*Organization*: The University of Western Australia*References*: <edadqd$pgc$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <edadqd$pgc$1 at smc.vnet.net>, Sergio Miguel Terrazas Porras <sterraza at uacj.mx> wrote: > When I calculate the dot product of vectors {1,Pi/4,0} and {2,0,1} in > Cylindrical Coordinates Mathematica 5.1 returns the result Sqrt[2], when the > result should be 2. Notwithstanding several of the other responses, the result _is_ Sqrt[2]. When you write {1,Pi/4,0}, surely you mean {rho, phi, z} == {1, Pi/4, 0} and _not_ that {x, y, z} == {1, Pi/4, 0} ? After loading Needs["Calculus`VectorAnalysis`"] and selecting Cylindrical coordinates, SetCoordinates[Cylindrical]; then in cartesian coordinates, this point is p1 = CoordinatesToCartesian[{1, Pi/4, 0}] {1/Sqrt[2], 1/Sqrt[2], 0} Similarly, p2 = CoordinatesToCartesian[{2, 0, 1}] {2, 0, 1} Hence the dot product of the coordinate vectors (relative to the origin {0,0,0}), computed in cartesian coordinates, is p1 . p2 Sqrt[2] This is the same result that you got, presumably using, DotProduct[ {1, Pi/4, 0}, {2, 0, 1} ] Sqrt[2] Of course, if you really mean {x, y, z} == {1, Pi/4, 0} then there is no need to load Calculus`VectorAnalysis`: the dot product is just {1, Pi/4, 0} . {2, 0, 1} 2 Note that Dot is _not_ modified when this package is loaded so Jean-Marc's response, Needs["Calculus`VectorAnalysis`"] SetCoordinates[Cylindrical]; {1, Pi/4, 0} . {2, 0, 1} is bogus -- the first two lines have no effect on the third. Modifying Andrzej's code, we have Simplify[(JacobianMatrix[] . p1) . (JacobianMatrix[] . p2)] Sqrt[2] Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul