# Kinetic energy of a body rotating on another rotating body

Consider a body which can freely rotate with respect to the inertial frame, and a rotating disk whose axis is fixed in body frame.

When applying the lagrangian method (does that make a difference?), is the kinetic energy of the disk with respect to the body frame (for constant disk rotation rate, the kinetic energy is constant) or with respect to inertial frame (for constant disk rotation rate, the kinetic energy depends on the rate of the parent body)?

Parent discussion: Defy gravity torques with gyroscopes?

• @MisterMystère, Why don't you use Euler equation ($\frac{d\vec{L}}{dt}=\vec{M}_{ext}$) instead of lagrange method. I think Euler equation will be much easier to handle for your problem. – Mas ooD Jul 7 '14 at 11:39