GYROSCOPES

Recall that using the Euler angles, a gyroscope moves through

and

The last rotation is the inner gymbal B which spins while B which spins while the outer loop remains constant. So, while the inner gymbal does not remain fixed in G, its planar axes in any direction are principal axes.

These equations are nonlinear and don't have a closed form solution.

STEADY PRECESSION

All that is needed is a moment about the y₂axis.

TORQUE FREE MOTION

J < I and β < θ

 

 

 

 

 

tanβ=J/I tanθ

J > I and β>θ