Abstract: The root loci analysis of the gyroscopic mechanical structural system controlled by a damper is presented. The breakaway points on the complete root loci are studied. It is pointed out when the damper is located on some position of the mechanical structural system, two branches of the root loci will meet at the breakaway point and then depart from this point in opposite directions. This result can play important role in determining the location and damping coefficient of the damper. Root loci breakaway analysis of gyroscopic mechanical structural system is studied via the numerical example of an axially-traveling string system.

Key words: Breakaway point, Damper, Root loci