# ROTATING SUBSYSTEM

When the relative motion in question (i. e. of the system w. r.t. FB) is that of a rigid rotating subsystem (such as an engine rotor or propeller in an air­craft or an inertia wheel in a spacecraft) with angular velocity wr relative to the main body, then we have, over the spinning component,

®в =

where Kfg is the position vector of a mass element relative to an origin anywhere on the axis of rotation. Ordinarily the mass center of the spinning body lies on its axis, and this is the natural choice of origin for RrB. In that case it is easily shown (an exercise for the reader) that the contribution of the rotor to h*, denoted hr, is

Кв=-?тв*»тв (б-4-24)

where •FTB is the inertia matrix of the rotor with respect to centroidal axes parallel to those of FB. If moreover the spin axis is a principal axis of inertia of the rotor the vector hr is collinear with tor, and has magnitude Irof where IT is the moment of inertia of the rotor about the spin axis. Naturally, there is one term like (5.4,24) for each rotor.