Effect of damping on the structure of the time-optimal control profile

A simple technique is proposed for the determination of parameters that correspond to the transition of one control structure to another. A damped floating oscillator is used to illustrate the procedure to determine the damping ratio that corresponds to the transition of a three switch to a five switch and a five switch to a three switch control profile. This technique can also be used to determine the maneuver that corresponds to the transition of a five switch to a six switch and finally to a seven switch control profile for a rigid spacecraft.