In the field of spacecraft altitude control and stabilization, the dual-spin maneuver has an important place. Here, we consider a problem which is a multibody analog of the dual-spin problem. The dynamical equations are derived using a modified form of the Euler-Lagrang equation on the special orthogonal group SO(3). It is then shown that with a suitable damping mechanism on one body and on the joint, an asymptotic stability theorem can be concluded by using the LaSalle invariance principle.