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Euler's equations for constant torque?

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data

    An axially symmetric space station (principal axis e3, and λ1 = λ2) is floating in free space. It has rockets mounted symmetrically on either side that are firing and exert a constant torque τ about the symmetry axis. Solve Euler's equations exactly for ω (relative to the body axis) and describe the motion. At t = 0 take ω = (ω1,0,ω3).

    As well I am told to introduce the constants
    3131

    α = (λ31)τ/(λ1λ3)


    2. Relevant equations

    SDkSib1.jpg
    n=ω1+iω2

    3. The attempt at a solution
    I tried several different things trying to solve the problem but unfortunately I could never quite figure out which parts of Euler's equation are zero. I think that the third τ in Eulers equation is zero which would make ω3 constant but then I'm not really sure where to go.
     
  2. jcsd
  3. Feb 10, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    x3 is the symmetry axis. The problems states that the torque τ is about this axis. That means that [itex]\Gamma[/itex]3 = τ
     
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