In the absence of an applied torque a rigid body with three distinct principal moments of inertia given by I1, I2 and I3 is rotating freely about a fixed point inside the body. the Euler equations for its components of its angular velocity (ω1,ω2,ω3)are
dω1/dt=[(I2-I3)/I1]ω2ω3, dω2/dt =[(I3-I1)/I2]ω1ω3 , dω3/dt =[(I1-I2)/I3]ω1ω2
the equilibrium points in(ω1,ω3,ω3) space are:
1. (1,-1,0) , (-1,0,1) , (0,-1,1)
2. (1,1,0) , (1,0,1) , (0,1,1)
3. (1,0,0) , (0,1,0) , (0,0,1)
4. (1,1,1) , (-1,-1,-1) , (0,0,0)
please explain the correct answer(option)