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How to find more solutions for an periodical equation with infinity solutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122900] How to find more solutions for an periodical equation with infinity solutions
  • From: Gy Peng <hitphyopt at gmail.com>
  • Date: Tue, 15 Nov 2011 05:50:12 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Dear all,

I have a matrix defined as:
Matrix[{\[Alpha]_, \[Beta]_, \[Gamma]_}, \[Theta]_] := {{\[Alpha]^2 \
(1 - Cos[\[Theta]]) +
    Cos[\[Theta]], \[Alpha] \[Beta] (1 -
       Cos[\[Theta]]) - \[Gamma] Sin[\[Theta]], \[A lpha] \[Gamma] (1 -
        Cos[\[Theta]]) + \[Beta] Sin[\[Theta]]}, {\[Alpha] \[Beta] (1 \
- Cos[\[Theta]]) + \[Gamma] Sin[\[Theta]], \[Beta]^2 (1 -
       Cos[\[Theta]]) +
    Cos[\[Theta]], \[Beta] \[Gamma] (1 -
       Cos[\[Theta]]) - \[Alpha] Sin[\[Theta]]}, {\[Alpha] \[Gamma] \
(1 - Cos[\[Theta]]) - \[Beta] Sin[\[Theta]], \[Beta] \[Gamma] (1 -
       Cos[\[Theta]]) + \[Alpha] Sin[\[Theta]], \[Gamma]^2 (1 -
       Cos[\[Theta]]) + Cos[\[Theta]]}}

Solve[{x, y, z} == Matrix[{0, 0, 1}, \[Theta]].{x, y, z}, \[Theta]]

I know this equation is periodical and has infinity solutions. So, Mathematica only gave me only one solution: {{\[Theta] -> 0}} and show me the message:

Solve::ifun: Inverse functions are being used by Solve, so some solutions
may not be found; use Reduce for complete solution information. >>

My question is, how could I see for example first 6 solution, because I
know the first 5 or 6 solutions should be different and then
repeat themselves periodically. What should I do to find the first 5 or 6
solutions?

Thank you very much!


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