Numerical Analysis of the Motion of a Rigid Body with an Attached Spring-Mass-Damper

This study analyzed the stability characteristics and the unstable motion of a rigid body with a spring-mass-damper unit nutation damper attached parallel to one of the systems principal axes. The equations of motion are presented and non-dimensionalized, and then numerically integrated over time. An analysis using a Liaponuv function develops the critical values of the moments of inertia for stability of the system, as well as the critical values of a dimensionless parameter k related to he spring constant. A discussion of the effects of the various parameters on the motion of the system is provided and some representative plots are included. The parameter b related to the distance of the nutation damper from ,,he principal axis is found to determine whether unstable motion approaches an apparent limit cycle, or a new principal axis. Parameter k affects the final position of the mass and can also influence the system toward limit cycle or equilibrium point motion. Parameter c representing the damping coefficient affects how quickly the system reaches its steady state motion. A summary of the unstable motions of the system and recommendations for further work are included