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MathGroup Archive 2007

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Re: Solve & RotationMatrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76082] Re: Solve & RotationMatrix
  • From: CKWong <CKWong.P at gmail.com>
  • Date: Wed, 16 May 2007 05:22:14 -0400 (EDT)
  • References: <f21g0q$7d6$1@smc.vnet.net><f23qq6$oa3$1@smc.vnet.net>

I've looked again at your algorithm & found that it was more
incomplete than I thought.

The following is a version that'll give you the answer =A3\ = 3=A3k/4, =A3] 0, A3^ = 0.  The formatting may seem horrible. Just copy it to mathematica and run
it.


\!\(\*
  RowBox[{\(=A3\ =. ; =A3] =. ; =A3^ =. ;\), "\n", \(VectX = {1, 0,
    0}; \), "\n", \(VectY = {0, 1,
    0}; \), "\n", \(VectZ = {0, 0, 1}; \), "\n", "\
[IndentingNewLine]",
    RowBox[{
      RowBox[{"RotX", "=",
        RowBox[{"(", GridBox[{
              {"1", "0", "0"},
              {"0", \(Cos[=A3\]\), \(-Sin[=A3\]\)},
              {"0", \(Sin[=A3\]\), \(Cos[=A3\]\)}
              }], ")"}]}], ";"}], "\n",
    RowBox[{
      RowBox[{"RotY", "=",
        RowBox[{"(", GridBox[{
              {\(Cos[=A3]]\), "0", \(Sin[=A3]]\)},
              {"0", "1", "0"},
              {\(-Sin[=A3]]\), "0", \(Cos[=A3]]\)}
              }], ")"}]}], ";"}], "\n",
    RowBox[{
      RowBox[{"RotZ", "=",
        RowBox[{"(", GridBox[{
              {\(Cos[=A3^]\), \(-Sin[=A3^]\), "0"},
              {\(Sin[=A3^]\), \(Cos[=A3^]\), "0"},
              {"0", "0", "1"}
              }], ")
      "}]}], ";"}], "\n", \(Rotation = RotX . RotY . RotZ; \), "\n
        ", \(PtO = {0, 0,
           0}; \), "\n
            ", \(PtA = {1, 0, 0}; \), "\n
              ", \(PtB = {0, 1, 1};\), "\n", \(VectN = \((
        PtA - PtO)\)\[Cross]\((PtB - PtO)\);\), "\n
          ", \(VectN = VectN\/\@\(VectN . VectN\)\),
    "\n", \(eq = \(VectN == Rotation . VectY // Thread\) // Simplify
\), "\n", \
\(eqS = eq /. {=A3] -> 0, =A3^ -> 0} // Simplify\), "\n", \(Solve[eqS, {=A3\}]
\)}]\)



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