A spacecraft system including a spacecraft assembly or "stack" having an upper stage of a rocket-powered launch vehicle providing a final boost phase during launch. The stack also includes a payload structure rotatably interconnected with the upper stage. The upper stage and the payload structure together define a central axis that is generally coincident with the thrust axis during launch. The stack has an axis of maximum moment of inertia that is not parallel to the central axis. The stack has internal damping such that unstable nutation occurs if the upper stage and the payload structure rotate together about the central axis at the same rotational rate and in the same direction. The system includes a controller that rotates the payload structure relative to the upper stage during the final boost phase to alleviate coning motion of the stack.