Stability of Steady-State Motion of an Isolated System Consisting of a Rotating Body and Two Pendulums

An isolated mechanical system consisting of a rotating body and two pendulums fit on its longitudinal axis is studied. This system models how pendulum, ball, or fluid (ring) dampers decrease or increase the nutation angle of a spin-stabilized artificial satellite. The conditions of origin, existence, and cessation of the steady-state motion of the system, depending on its parameters, and the stability conditions for the primary motion (the body rotates about the longitudinal axis and the pendulums lie on the same line) and secondary motions (the body does not rotate around the longitudinal axis) are established. The residual nutation angle is estimated. © 2014, Springer Science+Business Media New York.