# Euler's equations for constant torque?

1. Feb 10, 2013

### Luftwaff1e

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

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. Feb 10, 2013

### TSny

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